Enter these codes when selecting a boxer at the Character selection screen in Two player arcade mode

Fight in the two-tier arena
Hold L.

Fight in the championship arena
Hold R.

Fight in the gym
Hold L + R.

Fight in the outdoor ring
Hold X + L + R.

Champ class boxers:
POD 5!

Gold class boxers:
MOSMA!

Silver class boxers:
RUMBLE BUMBLE

Bronze class boxers:
RUMBLE POWER