Level select
Enter sound test mode from the options screen. Play sounds 8, 4, 19, and 71 in that order. The screen will flash to confirm correct code entry. Begin game play, pause, and hold [Down] + [A] + [C] to display the level select screen.
Invincibility
Press [Left]x2, [A], [B], [C], [Left], [Up], [Down], [A], [Right], [A] at the title screen. A sound will confirm correct code entry.