Level Skip and Invincibility: (Unconfirmed)
Source: GamePro - April 1996 - Page 124
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Level Skip: At the Press Start screen, press button A, B, Right, A, C, A, Down, A, B, Right, A.  Start a game and pause it.  While the game is paused, press Button A to warp to the next level.

Invincibility: At the start of level 2, collect seven stars and go back to the toy box at the beginning of the level.  Jump in the box and crouch down until the star in the upper-left corner spins.  You are now invinsible.

Game Genie Codes:
Source: GamePro - July 1996 - Page 120
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BJDA - AA7A - Infinite Lives
G2YA - AA7G - Invulnerability
CEBT - AAGJ - Start on level 18