Boxer

Often seen as a last resort in combat, one's fists are considered crude and more useful for other purposes than direct damage. Boxers ignore this view over their art and raise their fists as a knight would raise their blade. Each with their own styles inspired by the races who in a lack of better term just "get it". The brutal reckless punches of the Orcish style, The precise and hard-to-master movements of the Goliath style, The low blows and cheap shots of the Goblin style and the well detailed techniques extensively written about by humans. Expert boxers train in all these styles to always be able to throw something new at their enemy. 

Proper Technique

When you choose this archetype at 3rd level you learn the basics of fightning bare fisted. Your unarmed strikes deal 1d6 instead of the usual 1 and your fists count as light weapons.
In addition as a boxer you learn certain Techniques fueled by Style Points. 

Style Points. You can use these point to perform special Techniques, You gain 3 points now and gain 1 additional point at each level.

Techniques. You learn to perform Special moves to empower your unnarmed attacks. Each Technique costs Style Points which will be listed in their description. Certain Techniques require a creature you are attacking to make a saving throw against your Style save DC. You learn techniques as you learn new fighting styles. You learn fighting styles at levels 3, 7, 10 and 15.

Style save DC. = 8 + STR + Profficiency bonus.

Street Style

A very crude but effective style. Street style is used by the less trained ruffians and rioters of major cities. You learn 3 techniques from this style.

Bob and weave. Whenever you strike an opponent with an unarmed attack you can spend 1 style point to dodge as a bonus action.

Sweep the leg. You can spend 1 style point to replace one attack with a leg sweep. If the creature is one size category above you or smaller the creature must make a Strenght saving throw against your Style save DC. If the creature is larger than you it has advantage on the save.

Distraction. When you miss an unarmed strike you can spend 2 style points to disengage as a bonus action.

Orkish Style

Focusing on sheer power over accuracy, it seems crude and brutal from the outside but the true subtlety of Orcish unarmed combat lies in winning a battle before the opponent even had a chance to fight back.
At 3rd level you learn to punch like an orc so your unarmed attack damage is increased to a d8. You gain 3 Techniques from this style.

Reckless Strike. You can spend 1 style point to attack with advantage but all attacks made towards you until the start of your next turn are done with advantage.

Crushing Blow. When you hit with an unarmed strike you can spend 1 style points to add your proficiency bonus to your damage.

Counter Attack. When someone misses a melee attack against you, you can use your reaction and 1 style point to make an attack of opportunity.

 

Goliath Style

A style made for competitive fights. From punching bears to fight pits, this style has proven itself time and time again. Focusing on defence and endurance this style grants it's users powerful talents.
At 10th level your unarmed strikes count as magical for the purpose of overcoming resistance and immunity to nonmagical attacks and damage. Your learn to punch with the power and precision of a goliath, your unarmed attacks do 1d10 + Str. You learn 3 new techniques from this style.

Magical Endurance. Whenever you take damage as a reaction you can spend 1 style points to grant yourself resistance to the damage taken, this resistance lasts until the end of next round.

Discombobulate. You can spend 1 style point to replace one unarmed attack with a disorienting strike that deals only your strength modifier's worth of damage and forces the target to make a Constitution saving throw or have disadvantage on all actions and attacks until the end of your next turn.

Aggressive Leap. You can spend 1 style point to leap and sprint towards your target, you can move 30 feet towards an enemy as a bonus action. if you move at least 15 feet in a straight line when making using this technique you do an additional dice of damage on your next attack on that turn.

Goblin Style

Considered as a style for cowards, the goblin fighting style incorporates less than honorable ways to defeat your opponents. 
At 15th level you learn to aim for the exposed weak spots, your unarmed attacks do 1d12+Str. You learn 3 techniques with this style.

Sand Attack. For 2 Style points you throw a fistful of sand, iron shavings, saw dust or anything you can find nearby into your enemy's eyes, forcing them to make a Dexterity saving throw or be blinded for a minute or until they use an action to clean their eyes.

Cheap Shot. For 3 style points you can punch an enemy in the same spot over and over and over again. You choose one creature that you can see and your attacks deal an extra 1d4 blundeoning damage and the damage increases by 1d4 for every time you hit the target. This lasts for 2 minutes or until you attack another creature or don't attack the target for 1 whole round.

3rd Arm. When you are the target of a melee attack you can use your reaction to use 2 style point to redirect the attack to another creature within 5 feet of you.

Tireless

At 18th level whenever you roll initiative without having any style points left you regain 4 style points and 1 use of second wind.