One hit kills
Press Up(2), Down(2), X, Y, Y, X at the main menu. A message will confirm correct code entry. Repeat the code for slow deaths.

Toggle unlimited supers
Press Up(2), Down(2), A, X, A, X at the main menu. A message will confirm correct code entry.

Toggle AI
Press Up(2), Down(2), A(2), B(2), X(2), Y(2) at the main menu. A message will confirm correct code entry.

Fight as Bastion
Successfully complete the game story mode as Magneto without losing any matches to face Bastion. Defeat Bastion to unlock him as a selectable character.

Fight as Bishop
Successfully complete the game in arcade mode as Gambit to unlock Bishop as a selectable character.

Fight as Blob
Successfully complete the game in arcade mode as Bishop to unlock Blob as a selectable character.

Fight as Psylocke
Successfully complete the game in arcade mode as Betsy to unlock Psylocke as a selectable character.

Fight as Dark Phoenix
Successfully complete the game in arcade mode as Phoenix to unlock Dark Phoenix as a selectable character. Alternately, successfully complete the game in story mode as Magneto.

Fight as Sentinel A
Successfully complete the game in arcade mode as Cyclops.

Fight as Sentinel B
Win twenty matches in survival mode.

Third costume
Successfully complete the game in story mode to unlock that character's third costume.

Fourth costume
Win twenty matches in survival mode with all characters.

Fifth costume
Successfully complete the game in arcade mode under the hard difficulty setting with all characters.

Sixth costume
Defeat all ten fighters in time attack mode in under fifteen minutes to unlock the sixth costume for the fighter you selected.

Seventh costume
Select team mode and choose to fight with eight characters. Defeat all of the your opponent's team by using two or less of your own fighters to unlock the seventh costume for the character(s) you used.
 

Wolverine gets his original yellow/blue/black costume.
Phoenix gets a red/gold costume similar to Dark Phoenix.
Juggernaut, Gambit, and Psylocke get a costume similar to their comic book original.
Beast gets a blue costume with a yellow X on his chest, and he also has a helmet.

When you chose the seventh costume for Cyclops, Wolverine, Betsy, Juggernaut, Sentinel A (Sentinel), Gambit, Storm, Sabretooth, Rogue and Magneto, they will most commonly appear in their costumes if they were in a "Vs." series game (Marvel vs. Capcom: Clash Of The Superheroes, X-Men vs. Street Fighter, X-Men Children Of The Atom, Marvel Super Heroes vs. Street Fighter).

Eighth costume
Win forty matches in survival mode as any character.

Classic costumes
Some characters have classic outfits that resemble the classic X-Men characters:

Wolverine: Costume VII
Betsy: Costume VII
Forge: Costume VI
Gambit: Costume V
Juggernaut: Costume VII
Magneto: Costume VII
Nightcrawler: Costume VII
Sabretooth: Costume III
Rogue: Costume VI

Ending sequences
There are three possible endings in the game in story mode.
 

Regular ending (Magneto's Victory): Defeat Bastion as Magneto.

Alternate ending (Phoenix's Victory): Lose the Magneto vs. Bastion fight and you will go to the Phoenix vs. Bastion fight. Defeat Bastion as Phoenix.

Secret Ending (Fury of Dark Phoenix): Get a "Perfect" victory in the Phoenix vs. Bastion fight. This will also, unlock Dark Phoenix as a playable character.

Nightcrawler: Play in the Dimensional Rage
When in training mode as Nightcrawler, turn on "Infinite Specials" then perform the Dimensional Rage technique. You will be in the Dimension for the technique. Perform a different special other than Dimensional Rage and make it contact. This will cancel Dimensional Rage and leave you in the darkness. To exit, perform the Dimensional Rage again and let it finish properly.