The purpose of this class is to capture my favorite elements of the Pathfinder Alchemist in a way that is (hopefully eventually) compatible with the D&D Beyond Subclass functionality. So, I'm putting this first version up for feedback and advice on what is and isn't possible.

Flavor: Taking the Rogue Arcane Trickster as a base, the alchemist casts spells by throwing explosive vials, and relies on their heightened agility to evade the splashback.

Pathfinder Alchemists have elemental bombs, lots of spellcasting, poison resistance (and later immunity), and mutagens (temporarily boosting physical stats at the expense of mental stats). But because D&D Beyond doesn't allow editing of base class features, I tried to keep most of the base Rogue class features the same, and only add in stuff approximately equivalent to Arcane Trickster perks. So, this alchemist loses mutagens, and is only a 1/3 caster, but gets all of the evasive rogue traits. I'm not sure if it's possible to grant benefits at levels other than the base subclass levels (3rd, 9th, 13th, 17th) - if not, things could be moved around to line up strictly with those levels. Poison Resistance/Immunity seemed important as part of the flavor to me, so I removed the 10th level ASI and extra wizard cantrip to try and balance them out. The spell and discovery lists are drafts only, not exhaustive, needing more work - but I think there's enough to start with!

Feature Comparison to Rogue/Arcane Trickster (Replaced / Replacement, Removed, Added, Modified)

Features with an * come from the Arcane Trickster Archetype

1st Level: Proficiences, Sneak Attack / Bomb, Thieves Cant / Alchemy, Throw Anything

2nd Level: Poison Resistance

3rd Level: Spellcasting*, Mage Hand Legerdemain* / Lesser Discovery

8th Level: Discovery

10th Level: Ability Score Increase, 1x wizard cantrip, Poison Immunity

13th Level: Versatile Trickster* / Bomber's Eye

17th Level: Spell Thief* / Greater Discovery

20th Level: Stroke of Luck / Grand Discovery

Things I'm still working on

Bombs: I'm not sure whether bombs should be spells or weapons - I'd like them to have the 20/60 range of improvised weapons. And I'm not sure on the number per day, or if there should be any recovery with a short rest. Should it be a ranged attack (dex), or a ranged spell attack (int)? At the moment, I have it as a ranged weapon attack, but the save against damage is against the spell save DC.

How balanced are bombs? They trade precision for splash damage that can help or hurt if it hits allies, and don't need advantage on the attack but can only use a fixed number of bombs per day. It's magical elemental damage rather than piercing, but on par with low level cantrips which do the same.

Bombs do damage in d6s because the progression is already there in the rogue table, and because I have alchemist d6s I want to use in real life. A 1st level alchemist does 1d6 with a bomb + int, and can throw 2 per day - equivalent to the acid splash cantrip with a slightly bigger splash area. A 7th level alchemist does 4d6 with a bomb, and can throw 5 per day - equivalent to 5 potions of fire breath, an uncommon item, or a 7th level wizard casting all their spell slots as fireball (which has a bigger radius). A 15th level alchemist does 8d6 and can throw 9 per day - as much as a 5th level wizard's weakest fireball that they could cast 11 times.

Spellcasting: Uses a different spell list with a mix of wizard and cleric spells. The alchemist does not get enough spell slots to be the party healer. I don't think there's a mechanic for it, but for simplicity, I'd like them to have the same 20/60 range as bombs - representing how far an alchemist can accurately chuck a vial - but I don't think D&D Beyond can accommodate that. Overruling the base spells, all alchemist spells have SM (no V) components with a range of 20/60 (or you can cast them as self or touch spells). As for concentration - I think it's necessary for balance, you can't stack alchemist spells, but concentration is not required to maintain a spell (alchemist's can't lose a spell by failing a Constitution saving throw or taking damage). Not sure about a mechanic for ending spells early.

The alchemist spell list includes 5th and 6th level spells the alchemist doesn't get access to unless they use their discoveries to learn them.

Skills and Proficiencies: Not sure how to implement these - skills might have to be added manually to 1st level alchemists, since they can't select the subclass till 3rd level.

Name: Alchemist, or maybe Fireslinger to avoid confusion with the Artificer/Alchemist subclass.

Blending the stealth of a rogue with the fiery wrath of a wizard, alchemists are a study in contrasts fueled by reckless intellect. They are uniquely at home in the space between science and magic, capturing the power of the weave in potions and explosive vials rather than casting traditional spells.

You must have an Intelligence score of 13 or higher in order to multiclass in or out of this class.

Class Features
As an alchemist, you gain the following class features.

Hit Points
Hit Dice: 1d8 per alchemist level
Hit Points at 1st Level: 8 + your Constitution modifier
Hit Points at Higher Levels: 1d8 (or 5) + your Constitution modifier per alchemist level after 1st

Proficiencies
Armor: Light armor
Weapons: Simple weapons, bombs, hand crossbows, shortswords, improvised weapons
Tools: Alchemist’s supplies
Saving Throws: Dexterity, Intelligence
Skills: Choose four from Acrobatics, Arcana, Deception, Investigation, Medicine, Nature, Perception, Persuasion, Sleight of Hand, and Stealth

Equipment
You start with the following equipment, in addition to the equipment granted by your background:
A shortbow and quiver of 20 arrows or (b) a hand crossbow and quiver of 20 bolts
A scholar’s pack, (b) dungeoneer's pack, or (c) an explorer's pack
Leather armor, two daggers, and alchemist’s supplies

Expertise
At 1st level, choose two of your skill proficiencies, or one of your skill proficiencies and your proficiency with alchemist’s tools. Your proficiency bonus is doubled for any ability check you make that uses either of the chosen proficiencies.

At 6th level, you can choose two more of your proficiencies (in skills or with alchemist’s tools) to gain this benefit.

Bomb
Once per turn, you can rapidly infuse a vial with your magical essence to create a bomb. At 1st level, choose a damage type from acid, cold, fire, lightning, or poison. You learn the admixture alchemist spell of that type. It does not count against the number of spells you know.
As an action, you can prepare and throw a bomb up to 20 feet, shattering it on impact. Make a ranged weapon attack against a creature or object, treating the bomb as an improvised weapon. On a hit, the target takes 1d6 damage of the chosen damage type, plus bonus damage equal to your intelligence modifier. Each creature (excluding the target on a hit and including the target on a miss) within a 15-foot sphere centered on the target must make a Dexterity saving throw against your spell save DC, taking splash damage equal to the minimum bomb damage on a failed save, or none on a success.
The amount of damage increases as you gain levels in this class, as shown in the Bomb column of the Alchemist table. Beginning at 3rd level, you can learn admixtures; alchemist spells that modify the type and amount of damage of your bombs.
You may use a number of bombs per day equal to half your alchemist level (rounded up) +1. Once per day when you finish a short rest, you can choose to recover a number of expended bomb uses equal to half your alchemist level (rounded up). You regain all expended uses when you finish a long rest.

Alchemy
Once per long rest, you can use your alchemist's supplies to craft a common alchemical item up to the value of 50gp. This costs you half the value of the item in raw materials.

Throw Anything
You are proficient in throwing improvised weapons and add your intelligence modifier to damage done with splash weapons (such as an alchemist’s fire). This bonus damage is already included in your bomb feature.

Poison Resistance
Beginning at 2nd level, you have advantage on saving throws against poison, and you have resistance against poison damage.
 
Cunning Action
Starting at 2nd level, your quick thinking and agility allow you to move and act quickly. You can take a bonus action on each of your turns in combat. This action can be used only to take the Dash, Disengage, or Hide action.

Spellcasting
When you reach 3rd level, you learn how to cast spells by imbuing liquids with your own magical essence. To observers, you don't appear to be casting spells in a conventional way; you drink or throw vials infused with arcane energy. Your known spells represent the spells you have materials to create on the fly.

Tools Required
You produce your alchemist spell effects through your brews. You must have your alchemist’s supplies (your spellcasting focus) in hand when you cast any spell using this spellcasting feature (meaning the spell has an "M" component when you cast it). If a cost is indicated for a component, you must have that specific component before you can cast the spell. If a spell states that a material component is consumed by the spell, you must provide this component for each casting of the spell.
To cast a spell, you must spend an action to activate a spell vial and drink or throw it, depending on the nature of the spell. In effect, your spells all have an "M" component (the spell vial) and an "S" component (the act of drinking or throwing the vial), but no "V" component (you can cast spells silently). Your spells do not require concentration to maintain (they do not end if you take damage), but casting a second concentration spell while you have another active causes the first concentration spell to end.
Your spell vials are inert until you spend an action to activate them, and they lose their power after one round. To use a spell with a touch range, you may use your action to activate the vial, then pass (or throw) it to another creature to consume within that round.

Cantrips
You learn three cantrips of your choice from the alchemist spell list.

When you gain a level in this class, you can replace one of the alchemist cantrips you know with another cantrip from the alchemist spell list.

Spell Slots
The Alchemist table shows how many spell slots you have to cast your alchemist spells of 1st level and higher. To cast one of these spells, you must expend a slot of the spell's level or higher. You regain all expended spell slots when you finish a long rest.

For example, if you know the 1st-level spell Cure Wounds and have a 1st-level and a 2nd-level spell slot available, you can cast Charm Person using either slot.

Spells Known of 1st Level and Higher
You know three 1st-level alchemist spells of your choice.

The Spells Known column of the Levelling Guide table shows when you learn more alchemist spells of 1st level or higher. Each of these spells must be of a level for which you have spell slots. For instance, when you reach 7th level in this class, you can learn one new spell of 1st or 2nd level.

When you gain a level in this class, you can replace one of the alchemist spells you know with another spell of your choice from the alchemist spell list. The new spell must be of a level for which you have spell slots.

Spellcasting Ability
Intelligence is your spellcasting ability for your wizard spells, since you learn your spells through dedicated study and experimentation. You use your Intelligence whenever a spell refers to your spellcasting ability. In addition, you use your Intelligence modifier when setting the saving throw DC for an alchemist spell you cast and when making an attack roll with one.

Spell save DC = 8 + your proficiency bonus + your Intelligence modifier

Spell attack modifier = your proficiency bonus + your Intelligence modifier

Admixtures
Admixtures are spells that represent substances you can add to your bombs to modify them. You can learn an admixture at any time you could learn an alchemist spell of the admixture’s level. You cast an admixture by using one of your bomb uses. Certain admixtures have additional requirements or limitations as listed.

Lesser Discovery
At 3rd level, choose one of the following options.
Chameleon. Your skin changes colors to blend in with your surroundings on command. You gain proficiency with stealth or expertise if you already have proficiency.
Concentrate Poison. You may use two doses of the same poison to create a more potent version. Creatures saving against this poison roll with disadvantage.
Extend Potion. Three times per day, you can cause any potion you drink that does not have an instantaneous duration to function at twice its normal duration to a max of 24 hours. You regain all expended uses when you finish a long rest.
Lesser Spell Knowledge. Choose two alchemist spells of 2nd level or lower. You can cast each of these spells once per day, or one of these spells twice per day. These spells do not count against the number of spells you know. You regain all expended uses when you finish a long rest.
Poison Blood. Your blood becomes poisonous, though harmless to you. A creature that bites you becomes poisoned until the end of their next turn. A creature that swallows you becomes poisoned until you are no longer within that creature. Creatures that are immune to poison are unaffected.
Spontaneous Healing. Three times a day, as a bonus action, you can regain 5 hit points. You regain all expended uses when you finish a long rest. If you are at 0 hit points at the start of your turn, this ability automatically revives you unless all your uses are spent (this counts as your bonus action for the turn).

Steady Aim (Optional)
At 3rd level, as a bonus action, you give yourself advantage on your next attack roll on the current turn. You can use this bonus action only if you haven't moved during this turn, and after you use the bonus action, your speed is 0 until the end of the current turn.

Ability Score Improvement
When you reach 4th level, and again at 8th, 12th, 16th, and 19th level, you can increase one ability score of your choice by 2, or you can increase two ability scores of your choice by 1. As normal, you can't increase an ability score above 20 using this feature.

Uncanny Dodge
Starting at 5th level, when an attacker that you can see hits you with an attack, you can use your reaction to halve the attack's damage against you.

Evasion
Beginning at 7th level, you can nimbly dodge out of the way of certain area effects, such as a red dragon's fiery breath or an Ice Storm spell. When you are subjected to an effect that allows you to make a Dexterity saving throw to take only half damage, you instead take no damage if you succeed on the saving throw, and only half damage if you fail.

Discovery
At 8th level, choose one of the following options.
Breath Weapon Bomb. Instead of preparing and throwing a bomb, you may drink the components, mix them within your body, and then expel them as a breath weapon as a standard action. This breath weapon is a 15-foot cone. Each creature within the cone must make a Dexterity saving throw against your spell save DC, taking full damage as a direct hit on a failure, or half damage on a success. Unlike throwing a normal bomb, expelling a breath weapon bomb does not provoke attacks of opportunity.
Celestial Poisons. Poisons and poisonous bombs and spells you create can now affect Undead, Demons and Devils.
Spell Knowledge. Choose two alchemist spells of 4th level or lower. You can cast each of these spells once per day, or one of these spells twice per day. These spells do not count against the number of spells you know. You regain all expended uses when you finish a long rest.
Sticky Poisons. Poisons applied to weapons last a number of strikes equal to your proficiency bonus.
Wings. You gain a fly speed equal to your walking speed.

Poison Immunity
At 9th level, you become immune to poison damage and can’t be poisoned.

Magical Ambush
Starting at 9th level, if you are hidden from a creature when you cast a spell on it, the creature has disadvantage on any saving throw it makes against the spell this turn. Your bombs count as spells for the purpose of this feature.

Reliable Talent
By 11th level, you have refined your chosen skills until they approach perfection. Whenever you make an ability check that lets you add your proficiency bonus, you can treat a d20 roll of 9 or lower as a 10.

Bomber’s Eye
Starting at 13th level, as a bonus action, you may extend the range and long range of thrown objects by 10ft and give yourself advantage on your next attack roll on the current turn.

Blindsense
Starting at 14th level, if you are able to hear, you are aware of the location of any hidden or invisible creature within 10 feet of you.

Slippery Mind
By 15th level, you have acquired greater mental strength. You gain proficiency in Wisdom saving throws.

Greater Discovery
At 17th level, choose one of the following options:
Greater Spell Knowledge. Choose two alchemist spells of 6th level or lower. You can cast each of these spells once per day, or one of these spells twice per day. These spells do not count against the number of spells you know. You regain all expended uses when you finish a long rest.

Elusive
Beginning at 18th level, you are so evasive that attackers rarely gain the upper hand against you. No attack roll has advantage against you while you aren't incapacitated.

Grand Discovery
At 20th level, choose one of the following options.
Awakened Intellect. Your intelligence increases by 2, as does your maximum for that score.
Eternal Youth. You stop aging.
Spell Knowledge. Choose two alchemist spells of 4th level or lower. You can cast each of these spells once per day, or one of these spells twice per day. These spells do not count against the number of spells you know. You regain all expended uses when you finish a long rest.
Poison Touch. On a successful melee attack, you may afflict a target with a punishing poison. The target must make a Constitution saving throw against your spell save DC or become poisoned, taking 1d3 Constitution damage per round for 6 rounds. The target can repeat the saving throw at the end of each of its turns, ending the effect on itself on a success.
Regeneration. You regain 5 hit points at the start of your turn. If you have 0 hit points at the start of your turn, this feature automatically revives you.

 
Alchemist Spell List
Cantrips
Acid Splash, Blade Ward, Control Flames, Create Bonfire, Dancing Lights, Fire Bolt, Frostbite, Mold Earth, Poison Spray, Ray of Frost, Smoke Bomb, Spare the Dying, True Strike

1st Level
Absorb Elements, Acid Admixture, Cold Admixture, Cure Wounds, Detect Magic, Detect Poison and Disease, Disguise Self, Expeditious Retreat, Faerie Fire, Feather Fall, False Life, Fog Cloud, Fire Admixture, Heroism, Identify, Jump, Lightning Admixture, Longstrider, Poison Admixture, Protection from Evil and Good, Purify Food and Drink, Sanctuary, Sleep

2nd Level
Alter Self, Barkskin, Blinding Admixture, Blindness/Deafness, Blur, Concussive Admixture, Continual Flame, Darkvision, Detect Thoughts, Enhance Ability, Enlarge/Reduce, Hold Person, Invisibility, Levitate, Lesser Restoration, Protection from Poison, See Invisibility, Silence, Spider Climb

3rd Level
Blink, Clairvoyance, Feign Death, Fly, Gaseous Form, Haste, Inferno Admixture, Meld Into Stone, Protection from Energy, Remove Curse, Stink Admixture, Water Breathing, Water Walk, Vampiric Touch

4th Level
Arcane Eye, Control Water, Death Ward, Fire Shield, Freedom of Movement, Greater Invisibility, Polymorph, Stoneskin, Stone Shape

5th Level
Dream, Greater Restoration, Legend Lore, Modify Memory, Rary’s Telepathic Bond, Scrying, Skill Empowerment, Transmute Rock

6th Level
Create Homunculus, Eyebite, Flesh to Stone, Heal, Investiture of Flame, Investiture of Ice, Investiture of Stone, Investiture of Wind, Primordial Ward, True Seeing