Alternate costumes:
To unlock the alternate classic costumes successfully 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.
Defeating Sentinels:
With Wolverine (at a high level) run behind the Sentinel. Select the Brutal Slash attack (R2 + X) and repeat it until the Sentinel falls.
Artwork:
To unlock the artwork collect all 19 Sketchbooks in Colossus' room.
Unlock Characters:
Do the following tasks to unlock the corresponding player
Beast - Successfully complete level 1.
Storm - Successfully complete level 1.
Ice Man - Successfully complete level 1.
Jean Grey - Successfully complete level 1.
Rogue - Successfully complete level 1.
Jubilee - Successfully complete level 2.
Nightcrawler - Successfully complete level 2.
Gambit - Successfully complete level 3.
Emma Frost - Locate Emma Frost in X Mansion after the Nuclear Facility level.
Colossus - Successfully complete the Nuclear Facility level.
Cyclops - Defeat Mystique in the New York City Riot level.
Magma - Successfully complete Magma's second training round.
Professor X - Enter the Astral Plane for the first time.
Psylocke - Successfully complete the New York City Riot level.