Instructions
Complete the first mission of the game called "You Can Bank on Batman." Return to the Bat Cave. Go right and get onto the rising platform.
Go right from the platform and stay on the upper walkway. Walk up to the computer on the far right side of the screen. There is also a computer in the center of the room, but you don't need it now. Press the switch by the computer to change over to the Arkham Asylum and the Villain missions.
Go left and through the door. Head south, then left again through another door. You'll be in a room with an armored van, the Penguin's sub and the Joker's helicopter. Walk all the way to the left to get to the Joker's helicopter.