Play as Psylocke:
Beat the game with Wolverine in arcade mode to unlock Psylocke.

Play as Juggernaut:
Beat the game using all default characters and Psylocke in arcade mode to unlock Juggernaut.

Play as Professor Xavier:
Beat the game with Juggernaut. Then, highlight Magneto and hold L1 at the character selection screen.

Play as Spider-Man:
Fight in arcade mode until you face Spider-Man. Defeat him and finish arcade mode. Then, highlight Cyclops and hold L1 at the character selection screen.

Alternate Costumes:
Play through academy mode with any character to get that characters alternate costume. When you choose your guy hold R1 and press square if they were in the first game, If they weren't hold R1 and press X.

Unlock Everything:
At the title screen press select, down, R2, L1, R1, L2 This will unlock everything for everyone.

Pool Party:
Put in the unlock everything cheat and then in 2 player you can go to the Pool Party as your stage. Everyone is equiped with a funny costume.

Thanks to Revolution readers marc aguihon, jacob and Karl!