Accomplish the indicated achievement to get the corresponding number of Gamerscore points:

Super strike expert (5 points): Perform all super strikes.
Relentless (5 points): Beat your own record 3 times against the same opponent.
Bronze legend (5 points): Win 10 fights.
Combo expert (15 points): Perform all combos.
Humiliation (15 points): Finish off the fight with a combo.
Silver legend (15 points): Win 30 fights.
I don't like skinny guys (15 points): Beat lightweight opponents 30 times.
I don't like big guys (15 points): Beat heavyweight opponents 30 times.
I don't like medium guys (15 points): Beat mid-weight opponents 30 times.
That's an eyeful! (15 points): Blind an opponent 20 times.
Under the Wire (20 points): Win a round with less than 10% of your life remaining.
Back to the sandbox (20 points): Win 20 fights against Ratface.
Your tricycle's waiting (20 points): Win 20 fights against Rider.
Get lost (20 points): Win 20 fights against Mover.
Reap the whirlwind (20 points): Win 20 fights against Jawbreaker.
Adios amigo (20 points): Win 20 fights against El Luchador.
Forsaken by the gods (20 points): Win 20 fights against Kawharu.
Tail between your legs (20 points): Win 20 fights against Jackal.
Saturday night fighter (20 points): Win 20 fights against Deadlock.
Tarred and feathered (20 points): Win 20 fights against Piston Joe.
Fallen angel (20 points): Win 20 fights against Angel Face.
The chips are down (20 points): Win 20 fights against Gambler.
Hang up your gloves (20 points): Win 20 fights against One Jab.
Combo master (20 points): Perform 50 combos.
Super strike master (20 points): Perform 50 super strikes.
Speed champion (20 points): Win 20 fights within two rounds.
Speed expert (20 points): Win 40 fights within two rounds.
Gold legend (30 points): Win 100 fights.
Platinum legend (30 points): Win 150 fights.
Speed master (30 points): Win 80 fights within two rounds.
Ratface's nightmare (20 points): Win 20 fights against Ratface in the open league.
Rider's nightmare (20 points): Win 20 fights against Rider in the open league.
Mover's nightmare (20 points): Win 20 fights against Mover in the open league.
Jawbreaker's nightmare (20 points): Win 20 fights against Jawbreaker in the open league.
El Luchador's nightmare (20 points): Win 20 fights against El Luchador in the open league.
Kawharu's nightmare (20 points): Win 20 fights against Kawharu in the open league.
Jackal's nightmare (20 points): Win 20 fights against The Jackal in the open league.
Deadlock's nightmare (20 points): Win 20 fights against Deadlock in the open league.
Piston Joe's nightmare (20 points): Win 20 fights against Piston Joe in the open league.
Angel Face's nightmare (20 points): Win 20 fights against Angel Face in the open league.
Gambler's nightmare (20 points): Win 20 fights against Gambler in the open league.
One Jab's nightmare (20 points): Win 20 fights against One Jab in the open league.

Additionally, there are eight secret achievements:

The killer shout (5 points): Use a super strike.
It's a long way down (5 points): Knock an opponent to the ground.
Once upon a time... (5 points): Perform a combo.
The Sandman (5 points): KO your opponent while he's groggy.
Young hopeful (30 points): Win League 3.
Rising Star (40 points): Win League 2.
King of the world (70 points): Win League 1.
Everyone's Nightmare (50 points): Defeat all opponents 20 times each.