Go to the title screen and press Up, Right (9 times), Down (6 times), Left (7 times), Z, X, Y, Y, Y, Z! I guess they wanted to make sure that you never hit it by accident.
Go to the title screen and press: Left, Up, Right, Down, Down, Right, Right, Up, R-Trigger. The screen will say 'Betsy's Room' and you can now select your level.
Fight the boss:
Highlight the stage you want. Now press: Left, Right, Right, Up, Right, Right, Up, Down, Right, Right, Up, R-Trigger. Now you can select the boss for that stage.
Thanks to Revolution reader Melvin P. Rhedd!