Complete certain monsters all the way to Tokyo's three stages:
Godzilla1st. Beat the game as Godzilla
GodzillaUSA Beat the game as Godzilla1st
Minilla Beat the game as GodzillaUSA
Dr. Serizawa Beat the game as Minilla
All VMU Monsters
At the VS Battle Menu select the bottom option and hold X Y and press Down L R. This will unlock up to 44 monsters but less than 10 will appear in the VMU.