Invincibility: At the title screen, press Up, Up, Up, Up, Down, Left Right, Up, then press start.
Level / Stage Select: At the title screen, press Up, Down, Left, Right, B, B, B, B, then press start. Use the select button to choose a stage and press A to start the stage.
Continue after game over: At the game over screen, hold down A, B and select and press start.