After meeting up with Catwoman, who is being held hostage by the Riddler, he will mention that a new trial is available to you in Chinatown. Get in the elevator with the Batmobile and you'll be thrown right into the next puzzle at the bottom. As soon as you enter, there will be a ramp to your left and another to your right; go up the one on the left. Keep going up and you'll notice a Riddler button, which seems to activate something nearby.
This Riddler button makes a platform come out in between two Riddler-activated ones (the red and white ones). Next to this button will be a seesaw one, with a big, red button, that makes the previous one retract back into the wall. First, get on the seesaw with the Batmobile so that it's going upwards and then press Circle to make the white platform stick out. What this does is make a small white piece pop out underneath the seesaw, making it stay in place as you drive the Batmobile up it.
Do just that and park it right before the first red platform. Get out and run down to the first switch as Batman, stepping on it to activate the thing. Using the Batmobile Remote, cross the red and white platforms to the other side, then go back to red. Get on the next seesaw and make it point upwards, then go back to white to lock it into place. Although it might hard to see, there is a small ledge at the bottom of the seesaw that you can use to build up speed, as you need to boost your way to the top and jump over the large gap to the last white platform.
If successful, drive around the corner and you'll find something to attach your winch to, which supplies power to the switch that you saw when you first entered this area. Go down to it and once Eddie activates it, stand on it to make some red lights, with one green one, light up. As the Riddler so astutely points out, this makes a series of glass cases spring up back at the orphanage, where Catwoman is located. Only one of the cases holds the key needed to help set her free, while the rest will...kill her.
The glass cases are set up in the same pattern as the lights on the switch where Batman is. Press L1 to switch to Catwoman and walk around them until you have them situated in the same design as the lights. With that done, locate the glass case that corresponds to the green light and walk up to it, grabbing the key inside, which reduces the counter on Catwoman's collar by one (with a freebie thrown in by the Riddler...how nice of him). Once you're finished, it's time to start the third riddle.
