Big head mode:
Beat the game on easy. Then, press X, A, Y, B, B, B, Up, Up, Up, Up, Up on controller D.

Mirror mode:
Beat the game on the normal. Then, press L, Left, L, Right, L, Down, L, Up, R, Left, R, Right, R, Down, R, Up on controller D.

Random mode:
Beat the game on the hard. Then, press B, Left, X, Y, X, Y, B, A, B, A, Right, Left, Right, Left on controller D.