Using story mode can result in these different endings

Magneto Victory Ending - Defeat Bastion using Magneto

Secret Ending - Achieve PERFECT victory in the (Phoenix vs Bastion) fight and you should unlock Dark Phoenix

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

Win twenty matches in survival mode.

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

Win twenty matches in survival mode with all characters.

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

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

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.

Eighth costume:

Win forty matches in survival mode as any character.