Master Cheat Unlock:
Go to the main menu and HOLD L and press Right, Right, left, Left, Down, Up, B.

Get Dark Phoenix:
Beat Arcade Mode using Phoenix

Get Bishop:
Beat Arcade Mode using Gambit

Get Psylocke:
Beat Arcade Mode using Betsy

Get Bastion:
Finish Story Mode using Magneto without losing any matches. You should fight Bastion. Defeat him to unlock him (keep in mind you only have one chance if lose you will have to do the whole story over)

Get Bishop:
Beat Arcade Mode using Gambit

Get Blob:
Beat Arcade Mode using Bishop

Get Sentinel A:
Beat Arcade Mode using Cyclops

Get Character's 3rd Costume:
Beat Story mode using any character

Get Character's 6th Costume:
Beat 10 characters in time attack mode using any character in under 15 minutes

Get Character's 7th Costume:
Use team mode and fight with 8 characters. Defeat the entire opponent team by only using 2 or more of your characters to unlock the 7th costume for the characters 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.

Various End Sequences:
Using story mode can result in these different endings

Magneto Victory Ending - Defeat Bastion using Magneto

Phoenix Victory Ending - If you lose the Magneto vs Bastion fight you can fight Phoenix vs Bastion

Secret Ending - Get a PERFECT victory in the Phoenix vs Bastion fight and you will unlock Dark Phoenix