Cheat mode
Press Start at the title screen. Press Up, Left, Right(2), Up when the "Game Start" and "Config Mode" options appear. The sound of an explosion will confirm correct code entry. Press Left or Right when "New York - Stage 1" appears to change the starting level.
Extra difficulty levels
Press Start at the title screen. Press Up, Down, Left, Right, Down, Start when the "Game Start" and "Config Mode" options appear. The sound of an explosion will confirm correct code entry. New difficulty levels will now be available. The "Training" difficulty setting will allow the game will continue from the last point played instead of restarting at the beginning of the level.
Invincibility
Press Left, Right, A + B + C at the main menu. A sound will confirm this part of the code. Then, press B, A, C, A, Left(2), Right, Left.