Unlock new modes:
Beat "A New Journey" to unlock Arcade Mode, First Person View, Parts Index, and The Grand Battle.
Change level appearance:
In VS mode, highlight Basic Arena or No Man's Land and press Z.
Dark Star VS mode level:
Play 50 matches in VS mode.
VS battle CPUs:
Beat Story mode.
In Grand Battle, go to Bogey's Café. Now go behind the counter look on the shelf.
Get a gold trophy in all Amusement Park tournament cups. Then, talk to the policeman at the front gate.
Thanks to Revolution readers chewbacca, ou812 and Forther!