Twenty dragons:
Begin game play and defeat the first Boss. Intentionally lose the game, then hold A + B and press Start at the title screen.
Sound test:
Hold A + B + Up on controller two and press the Reset button on the NES. Use controller one to select various game sounds.
Gold Dragon:
Intentionally die during the battle with the first Boss to get the Gold Dragon.
Level select:
Hold A + B + Up on controller two and press the Reset button on the NES. Then, press B, Up(2), B, Down(2), B on controller two at the sound test screen. Press Left or Right to select a new starting level.
