Everyone and their mother knows about the Beastmasters issues and plenty of people have made their own versions... well here's another!!!

Taken straight from my own total reworked version of the Ranger class (Go to GMbinder and put this at the end):

/share/-LsJ92BURfzON8Z53l3W

I've taken from both the PHB and Revised Ranger UA (and a little from the Artificier). I've made it compatible with the PHB ranger class. I haven't had the chance to try it so any feedback is appreciated.

Beastmaster magic

Starting at 3rd level, you learn an additional spell when you reach certain levels in this class, as shown on the Beastmaster Spells table. The spell counts as a ranger spell for you and is always 

Beastmaster Spells

* Familiar is Fey.

Animal whisperer

Beginning at 3rd level, You have an innate ability to communicate with beasts, and they recognize you as a kindred spirit. You gain proficiency with the Animal Handling skill if you don't already have it, otherwise you gain proficiency in a skill of your choice. Your proficiency bonus is doubled when using the Animal Handling skill as long its not being doubled by another ability.

Animal Companion

At 3rd level, you learn to use your magic to create a powerful bond with a creature of the natural world.

Choose a beast that is no larger than Medium and that has a challenge rating of 1/2 or lower and that isn't a swarm of beasts.

If you already have an beast NPC that is friendly to you that fits the criteria and that you want to bond with, it automatically gains all the benefits of your Companion’s Bond ability. Otherwise you can spend 1 hour of work to call forth an animal from the wilderness to serve as your faithful companion. Work with your DM to see what beasts may be available in the area.

At the end of the hour, your animal companion appears and gains all the benefits of your Companion’s Bond feature. You can have only one animal companion at a time. If your animal companion is ever slain, the magical bond you share allows you to return it to life. If the beast has died within the last hour, you can use your action to touch it and expend a spell slot of 1st level or higher. The beast returns to life after 1 minute with all its hit points restored. If the beast has been dead for more then an hour, or you do not have access to any part of it's body, you can spend 1 hour and a spell slot of 1st level or higher to call forth your companion’s spirit and use your magic to create a new body for it.

At the end of a long rest, you can choose to gain a new animal companion. If so, your current companion leaves you and your Companions Bond feature transfers to the new companion

At level 3, total damage done from your companions attacks do half the amount they would normally do and the DC of any abilities that would cause a saving throw, such as a Wolfs bite attack, is set to 10.

If you are level 5 or higher, your companions damage is no longer halved and any possible DC becomes whatever number is appropriate for it.

CR 0 and 1/8 companions:
When choosing a beast companion, it's recommended to pick a companion thats CR 1/4 or 1/2.

CR 0: CR 0 monsters are incredibly weak even with the boosts the Beastmaster subclass gives. If you do want to use a CR 0 monster perhaps a higher CR beast can fulfill what you're looking for. For example, instead of a Weasel companion, take a Giant Weasel. Also some lower CR beasts can be reskined using higher CR beasts. For example, instead of using the Hyena and Jackal stat blocks, you could use the Wolf stat block as all 3 have similar abilities and skills.

CR 1/8: Most CR 1/8 beasts are substantially weaker even with the boosts the Beastmaster subclass gives. If you do want to use a CR 1/8 beast, you may apply the following to them:
They gain one Ability Score Improvement but can't raise an ability score past 16 and the damage die they use for their physical attacks is increased by one.

For example: A Flying Snake would do 1d4 damage with its bite instead of 1 damage ( the poison damage it does is unaffected) and a Giant Rats bite attack would do 1d6 damage instead of 1d4.

This should help bring them to a similar level to CR: 1/4 beasts.

 

Companions Bond

Your animal companion gains the following abilities and game statistics, some determined in part by your level:

• The animal companion loses its Multiattack action, if it has one.

• The companion adds your proficiency bonus in addition to where it normally applies its proficiency bonus, apply it also to the beasts AC and damage rolls. When your proficiency bonus increases, apply the changes to the following areas: AC, attack and damage rolls, as well as to any saving throws and skills it is proficient in.

• Your companion has an amount of hit dice (d8's) equal to your ranger level in addition to the hit dice it originally had. Your companion regains all lost hit points after it finishes a long rest and can spend Hit Dice during a short rest. Its hit point maximum equals either the amount listed in its stat block or 5 + five times your ranger level, whichever is higher. When your companion is reduced to 0 hit points, it must roll death saving throws instead of dying outright unless the damage taken reduced it to a negative amount larger the its hit point total.

• When using your Natural Explorer feature (if you have this feature), you and your animal companion can both move stealthily at a normal pace.

• Your companion becomes proficient in all saving throws.

• Any spell you cast that requires your companions Intelligence score to be within a certain range (like the Beast Bond spell) ignores this restriction.

• In combat, the creature shares your initiative count, but it takes its turn immediately after yours. It can move and use its reaction and bonus action on its own, but the only action it takes on its turn is the Dodge action, unless you take an action your turn to command it to take one of the actions in its stat block or the Dash, Disengage, or Help action. you can also verbally command the beast where to move on your turn (no action required by you). When you take the attack action on your turn, you can order the beast to take one of the actions it's capable of at the same time. When you gain the Extra Attack feature, your companion uses one of your attack actions to use an action it is capable of instead.

If you are incapacitated or absent, the beast acts on its own, focusing on protecting you and itself. The beast never requires your command to use its reaction, such as when making an opportunity attack.

Your companion shares your alignment, and has a personality trait and a flaw that you can roll for or select from the tables below. Your companion shares your ideal, and its bond is always, “The ranger who travels with me is a beloved companion for whom I would gladly give my life.”

 

D6	Trait
1	I’m dauntless in the face of adversity.
2	Threaten my friends, threaten me.
3	I stay on alert so others can rest.
4	People see an animal and underestimate me. I use that to my advantage.
5	I have a knack for showing up in the nick of time.
6	I put my friends’ needs before my own in all things.

 

D6	Flaw
1	If there’s food left unattended, I’ll eat it.
2	I growl at strangers, and all people except my ranger are strangers to me.
3	Any time is a good time for a belly rub.
4	I’m deathly afraid of water.
5	My idea of hello is a flurry of licks to the face.
6	I jump on creatures to tell them how much I love them.

Exceptional Training

At 7th level, while your companion can see you, it has advantage on all saving throws.

In addition, the beast's attacks now count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage.

Bestial Fury

Starting at 11th level, your beast companion can use the Multiattack action if it has one, otherwise it can make two attacks when you command it to use the Attack action.

Share Spells

Beginning at 15th level, when you cast a spell targeting yourself, you can also affect your beast companion with the spell if the beast is within 30 feet of you.