Successfully complete the game in all three modes to unlock an option that allows you to play as Itchy & Scratchy for one level, Kang for another level, and Smithers for another level.
Play through new challenger circuit mode and you will eventually fight Bumblebee Man. Defeat him and save the game to unlock him at the character selection screen.
Play through new challenger circuit mode and you will eventually fight Moe. Defeat him and save the game to unlock him at the character selection screen.