I recently got a collection of Batman comics where he fights the Riddler. He could use:
-A wooden puzzle pistol that shoots pink lightning for a super. This is from The Riddler's Prison Puzzle Problem.
-He could throw explosive puzzle pieces.
-He could stun the opponent with a giant crossword puzzle. These two ideas come from the Riddle-less Robberies of The Riddler.
-He could tie the opponent up with white metal wire. He's done that in a few issues.
-In a story in the silver age, The Remarkable Ruse Of The Riddler, he was able to immediately bounce back to his feet whenever he was punched by batman thanks to a button on his shirt. Maybe that could be a counter?
-He had also electrified his uniform in that comic. Maybe that could be something like blanka?