First enter in the password 1408, this will enable Cheat Mode which is accessed by controller 2. After turning on the cheat, you can use on of the following passwords to start on the level of choice. During gameplay, the Start button on controller 2 will pause without bring up the pause menu. The C button on controller 2 will restore Batman's health, the A button on controller 2 will skip to the next stage. And finally, the B button on controller 2 will show the end game credits.
First, use password 5257 as a password and on the bottom of the screen objects will appear confirming correct password entry. Then, Type in the password for what level you want to go to: