Once you've beat the game, press any button to continue to the Main Menu again. Now, when you start playing again, you'll be in a harder mode. The game won't tell you this, but you can see by harder enemies in the first stages who you'd normally come across only in later stages.
When your game is over and you're at the blue After Burner screen, press Left, Left, Left, B, B, B, A, A, A, Start. You will continue on the level you just got a game over on.
Before you turn on the game, press and hold down the b button, then turn on the game. You'll be able to listen to 5 songs.
Before starting your game, plug in a controller to slot 2. Hold A and B on that controller, and then tap START on the controller in slot 1.
Hold A + B on controller two and press Start on controller one.
Press A + B + Select at the game over screen.