Cheat mode:
Press Left, Up, Left(2), A, B at the main menu to display a cheat menu with level select, easy kill, and all weapons options.

Play as The Riddler:
Note: This code requires a six-button controller. Hold Up + X + B + A + C at the character selection screen. The Riddler will be controllable in training mode.

Extra strength:
Pause game play and press Up, Down, Left, Right, Up(2), Down(2), Left. The sound of an explosion will confirm correct code entry.

Special moves:

Bat Cuffs: Press Toward(2), C.
Electric Shocker: Press Toward, Down, C.
Holographic Decoy: Hold Down and repeatedly tap A.
Homing Batarangs: Press Down, Toward, B.
Leg Sweep: Press Toward(2), A.
Normal Batarang: Press Down, Toward, A.
Rocket Boots: Press Toward, C, Toward, B, Toward, C.
Smoke Bomb: Press Toward, Down, B.
Spin Kick: Press Down, Backward, C.
Stun Bomb: Press Down, Toward, C.
Super Shield: Repeatedly press B and C.

Hint: Defeating Big Riddle:
Enable the "Cheat mode" code. Select the "Easy Kill" and "All Weapons" options. When you fight the Big Riddle monster, throw the Batcuffs (Towards, Towards, C). This will immobilize the enemy, allowing you to pop him with an Uppercut (Down + A). Repeat this until the monster is defeated. Do not worry if he regenerates some of his strength. Just use the Batcuffs and Uppercut pattern.