This trail takes place in the tunnels under the Elliot Memorial Hospital, where you can have some problems locating the gate to the building's underground. Do not climb to the rooftop of the hospital and explore its lower levels. Here, you should find a small square, surrounded by huge indestructible barricades. The solution to this problem is looking around the area for the ramp shown in the above screenshot. Use the ramp (with the charger) to get near the garage.
If you still have not completed the Own the Roads side mission, it will be possible to drive into the garage only after you have neutralized the militia outpost here. Use the batmobile to knock out all of the opponents, find the leader (it is a good idea to use the detective mode here) and smash the controlling device that you find on him. Only after that, can you drive into the elevator, through the garage gate, and wait until you get to the location of the trial proper.
This trial is very similar to the first one, because you need to win three time trials. In this case, all three take place over the same circuit. With each successive lap, avoiding some of the obstacles will be a bit more difficult and you will also have less time to reach the finishing line.
The obstacles that you run into can be divided into two groups. The first one is movable elements of the ceiling which you need to manipulate with the Riddler blockade. It is very important here that you cannot activate the blockade while driving over red plates - at the beginning of each lap, drive into the side sections and later on, reach the safe spots. The other group is green blocks that slam into the ground on a regular basis. They are impossible to control in any way so, make sure that you drive flawlessly and steer clear of the green fragments of the track.
After you have won the three time trials, get out of the batmobile and go to the pressure plate. See the panel with the flashing bulbs, switch to Catwoman and find the correct capsule, basing on the panel readings - it has been shown in the above screenshot. After you have used the correct key, switch to Batman and go back to the surface.