Invincibility:
Pause game play and press R, Right, A, L, Right, A, Down, Y.

Level restart:
Hold L + Up until the game restarts the current level.

Level selection:
Pause game play and press L, A, Z, Y, Left, Right, A, Down, Right, L.

Free movement:
Pause game play and press L, A, Left, L, Right, Down(2). Resume game play. Hold Y while using the D-pad to move freely.