Go back to GCPD and talk to Gordon, who will begin going to the Clock Tower. You'll have to escort him there and you can't move very fast in the Batmobile at the moment, so you can full throttle it until some thugs in vehicles show up. This is the point where you need to take them out, with the quickest way to do that by side swiping their vehicle.
Once that's done, keep driving until Batman tells Gordon to get in the Batmobile, so pull into the marker on the ground, then Alfred will chime in and tell you about the militia presence on the three islands. Since you're on Bleake Island at the moment, all you have you worry about are 12 drones, all of which are guarding the Clock Tower. When you get there, you'll have to destroy all of them, so keep an eye out for their line of fire.
Head to the Clock Tower after destroying all of the drones, then grapple to the trap door at the top, only to be told you need to get rid of all of the thugs below before you can go inside. There are a total of six armed goons, one of which is a Medic, so he should take first priority. You have a lot at your disposal here, including vantage points, grates and even fragile walls, so experiment if you want to get some nice XP.
Go back to the top of the Clock Tower and enter via the secret door, where you'll see something that happened in the past. Keep walking around until the scenery eventually reverts back to the Clock Tower. Pick up the wheelchair when you see it and then Gordon will come up via the elevator. Well, things have gone from bad to worse it seems, so continue walking around until you can finally use the computer.
You will need to cycle through some footage to find out who took Barbara. Note that the instructions are in the lower right portion of the screen. Now, choose the upper right panel and rotate the right stick clockwise until you see two vehicles in the video. You will want to select the portion of that video with the red vehicle on the left, which is the one that took Barbara. Do that, initiate the shutdown via the same computer and head back outside to the Batmobile.
