Platinum mode:
Press X, B, L, R when "Press Start" appears at the title screen.

Flat mode:
Press Down, Up, B, X when "Press Start" appears at the title screen.

Big heads:
Press X, B, Up, Down when "Press Start" appears at the title screen.

Small heads:
Press X, B, Down, Up when "Press Start" appears at the title screen.

All boxers:
Win the Bronze, Silver, and Gold belts.

Mike Tyson Challenge:
Defeat Mike Tyson and win the Gold belt to unlock the undisputed champ mode..

Fight as Mike Tyson:
Win the Gold Belt to unlock Mike Tyson in single player mode.

Fight as Iron Mike:
Win the Mike Tyson Challenge to unlock Iron Mike, the early version of Mike Tyson.