Back at the orphanage, head through the door marked "Advanced Deathtraps" and have Batman stand on the switch right by the entrance. This will open a tiny spot just above the gate to your left, which Catwoman and get to by clinging to the ceiling just above both of you. Once you're in this area, have her stand on this switch in here to make the floor become electrified in both rooms. On the wall opposite of the entrance (on both sides) is a series of unlit bulbs on a question mark, with one of them being lit for now.
Each set will show the safe path that you can walk with the other character, and once you reach the end for a character, more of the safe path will be shown for the other. There's a slight twist, though, as once you get halfway through with a character, the board with the lights will begin spinning on that side, making things a teeny bit more awkward. Step on the switch at the end to deactivate the panels and once you hit both, some Riddler robots will appear. These carry the same red/blue colors as before, meaning you can only defeat those ones with their respective character. When you're done, grab the key and get ready for the final riddle.
