Cheat mode:
Press Left, Up, Left(2), A, B, Y at the game start screen. Change
the game type to normal mode and press Start. Choose a character
and press Start to display the cheat mode screen. This screen
allows stage selection, access to all weapons, and control of the
Riddler in the practice mode. 

Kill all enemies:
Enable the "Cheat mode" code. Press Start + L + R during game play
to kill all normal enemies. Press this sequence multiple times to
kill the Boss characters. 

Riddler's clues: 

"Unlucky ... baker's dozen"
Blast off the elevator's roof and use the grappling hook to
reach the 13th floor. 
"Steel ... fall through the floor"
Use the grappling hook to yank down the hanging safe and open a
secret room in Two-Face's hideout. 
"A musical ... rewards"
Knock an opponent into the electric cords on Claw Isle. 
"Looking ... found"
Save the hostages by raising your character up with the grappling
hook. 
Hint: Defeating Big Riddler:
To defeat Big Riddler in the final level, you must hit him with
contact hits. All other attacks do no damage. Use stick goo then
jump kick him. Repeat this until he dies.