Use the following codes at the cheat menu under the setup screen:
All Boxers: Start, A, Y, X, X, Z, Z, X, Y, A, Start
Invincibility: Start, A, A, Y, Y, Z, Z, X, X, Start
Intercontinental Tourney: Start, A, A, A, Y, Y, Y, X, X, X, Start
Conversation Mode: Start, Z, A, Y, X, Z, Z, Z, Start
Boxer's Life Mode: Start, A, X, Y, Z, A, X, Y, Z, Start
Scrap Yard Arena: Start, Y, Z, Y, Z, A, A, Start
Turbo mode: Start, A, Z, Y, X, Start
Rapid Power Up mode: Start, A, Y, A, Y, A, Y, X, X, X, Start