Select "Puzzle Mode". Then, press Left (2), Up, Down, L, R, L, R, L + R at the puzzle selection screen. Bub, Bob, and the Boss characters may be selected. You can also press Left (2), Up, Down, Left, Right, Left, Right, L + R at the puzzle selection screen to get the same effect.
Press L, Up, R, Down at the title screen. A creature will appear in the bottom right of the screen to confirm correct code entry. Select puzzle mode, then choose the new "Another World" option. You can also press A, Up, B, Down at the title screen to get the same effect.
Press Z+L+R+A during game play to enable level skip.
Press Z+L+R+A at the game selection screen.