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, , Up, , Right, , Down, .

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!