Double health/speed in Vs. Mode:
At the title screen, press Down, Down, Up, Down, Left, Right, Down, Up, Up, Up, Up, Right, Left, Square.
Extra Vs. Mode characters:
At the character select screen, press L1, L1, Down, Down, R2, Select, R2, Select, R1, L1, R2, R1, R1, Select.
Big characters at world map:
At the title screen, press Left, Square, Up, Circle, Right, Triangle, Down, Triangle.
Vs. Mode Elephant Pool Arena:
Win 20 team battles.
Vs. Mode Metal Age Arena:
Win 100 arena battles.
Thanks to Revolution readers chipperdan and eegloo!