Complete the following tasks to unlock the corresponding player in the game.

Unlock Beast:
Complete level 1.

Unlock Storm:
Complete level 1.

Unlock Iceman:
Complete level 1.

Unlock Jean Grey:
Complete level 1.

Unlock Rogue:
Complete level 1.

Unlock Jubilee:
Complete level 2.

Unlock Nightcrawler:
Complete level 2.

Unlock Gambit:
Complete level 3.

Unlock Emma Frost:
Locate Emma Frost in X Mansion after the Nuclear Facility level.

Unlock Colossus:
Complete the Nuclear Facility level.

Unlock Cyclops:
Defeat Mystique in the New York City Riot level.

Unlock Magma:
Complete Magma's second training round.

Unlock Professor X:
Enter the Astral Plane for the first time.

Unlock Psylocke:
Complete the New York City Riot level.

With Wolverine at a high level approach the sentinel from behind and then select the 'Brutal Slash' attack (R2 + X) and keep repeating until the Sentinel falls.

Alternate Costumes:
To unlock the alternate classic costumes complete the game.

Stat Increase:
To increase your characters' stats collect the hidden Comic Books.

Bonus Danger Room Tasks:
To unlock more tasks in the Danger Room collect the hidden Danger Room Discs.

Artwork:
To unlock the artwork collect all 19 Sketchbooks in Colossus' room.