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

Get In The Ring (5 points): Win a Fight Now match against the CPU.
Just Like Mike (40 points): Win a Fight Now match by KO in in the first round against the CPU in a 10 round fight.
More machine than man (50 points): Win 50 Fight Now matches against the CPU.
Knock a sucker out. (10 points): Win by a knockout in Fight Now against the CPU.
Ecko Trunk Challenge (15 points): Beat CPU Miguel Cotto in Fight Now on Pro.
Man Up Manny (15 points): Beat CPU Manny Pacquiao in Fight Now on Champion.
Pull No Punches (10 points): Win a Fight Now match vs the CPU while landing at least 500 punches.
Pound For Pound (40 points): Win a fight against a CPU opponent in a higher weight class than you.
The Road Is Long (10 points): Win 10 fights in Legacy Mode.
The Champ Is Here (40 points): Win a championship belt in a single weight class.
The Latest and the Greatest (50 points): Retire as a Superstar.
From Chump to Champ (20 points): Win the Amateur Tournament in Legacy Mode.
Movin' On Up (30 points): Move up in weight class in Legacy Mode.
Undefeated (20 points): Win 5 Consecutive Legacy Mode fights.
My Style Is Impetuous (60 points): Beat CPU Mike Tyson on G.O.A.T. using a created boxer in Fight Now.
XL (50 points): Win the Middleweight Championship Belt in Online World Championship Mode.
L (25 points): Win the Lightweight Championship Belt in Online World Championship Mode.
Solid Contender (30 points): Win 5 online ranked matches.
Pain Brings Glory (5 points): Win a match in Online World Championship Mode.
Comeback Kid (10 points): Win a Online ranked match after being knocked down twice.
Walk like ten men (10 points): Win 10 Fight Now matches against the CPU.
David and Goliath (40 points): Beat CPU Mike Tyson in Fight Now on G.O.A.T.
King of The Rope-a-Dope (40 points): Beat CPU Muhammad Ali in Fight Now on G.O.A.T.
Punch Drunk (10 points): Win a Fight Now match vs the CPU while landing at least 250 jabs.
Enough To Feed a Horse (10 points): Win a Fight Now match vs the CPU while landing at least 10 haymakers.
Precision Guided Pain (50 points): Win a fight where you landed at least 70% of your punches vs CPU.
GOAT (80 points): Retire as the G.O.A.T(unlocks achievements; Retiring as a Superstar and Hall of Famer if not earned).
Big Gloves to Fill (65 points): Retire as a Hall of Famer (unlocks achievement for retiring as a superstar if not earned).
Flyswatter (60 points): Beat CPU Muhammad Ali on G.O.A.T. using a created boxer in Fight Now.
XXL (75 points): Win the Heavyweight Championship Belt in Online World Championship Mode.
A Force to Reckon With (15 points): Win 10 online ranked matches.
New Blood (5 points): Import a boxer into Legacy Mode.

Additionally, there is one secret achievement:

You're In The Game! (5 points): Create a boxer using the Photo Game Face tool.