Start off by taking cover behind a small brick wall. Use the zoom function to monitor movements of a nearby guard. I would also recommend having the detective mode turned on, so it'll be easier to spot other goons. Obviously you'll have to wait for the first thug to stop looking your way. Once he's turned around head towards the second brick wall located closer to his position.
There's an entrance to a ventilation shaft to your left. Wait for the guard to turn around for the second time and approach the grating quickly. Press the action key to get rid of the obstacle and enter the ventilation shaft. You'll have to use the hook when you exit the tunnel which shouldn't be a problem.
Eventually you should be able to locate a second ventilation tunnel. Walk through it and kick the grating at the end. You'll find yourself in the top section of the room and obviously it's going to be easier to monitor enemy movement from here. Proceed to your left (screenshot #2).
Approach the ledge while holding the run key and Batman should automatically glide towards a lower platform located in front of you. Grab the nearest ledge, however don't pull yourself up right away. Instead turn on detective mode and wait for a nearby guard to start moving the other way (a little to your right).
Make a few steps forward and drop down to a lower platform. You should now consider grabbing a new ledge. Remain in this position and begin moving to your right. You can't jump over the railing, because you would have nowhere to hide. Keep heading right until you come across a wall. You'll now have to decide how you want to proceed.
The first method would require you to climb up to the balcony and to use a nearby ladder (screenshot #1). The biggest disadvantage is that you would have to avoid being seen by two guards at the same time (the one on the balcony and the one inside the control booth). The second method would require you to drop down to a lower platform and to use a small shaft (screenshot #2). The tunnel would lead you to an isolated area where you would have to use the hook several times.
It doesn't matter which method you'll choose, because both versions end the same way - with you performing a silent takedown on the inmate inside the control booth. Don't worry if you're seen from now on, because the guards are safe. If the guy from the lower balcony sees you wait for him to use the ladder and stun him immediately when he's near you. Otherwise return to the balcony and sneak up on him.
Aside from the enemies mentioned above, there are three more convicts for you to eliminate. In order to reach the first inmate you should use the nearest balcony. Make sure that he's looking the other way before attacking him. His buddy is standing nearby (screenshot #2), so it'll be even easier to neutralize him.
The final third opponent is patrolling the area beneath your current position. It would be a good idea to eliminate him without any additional delays, so he won't get spooked by the alarm. Eliminating all inmates will allow you to rescue the guards automatically. Talk to Robert Stirling and once you're done turn on the detective mode to continue with your investigation.
Eventually you should be able to find a hidden alcove in the wall. Remember that it can only be seen if you're using detective mode. Press the action key and use your sequencer on the panel. Just like when you were trying to disable the electricity you'll have to go through three stages in order to complete the mini-game.
Notice that hacking the panel has unlocked a nearby passageway. Use it and you'll end up standing in the Titan Production Facility. Make a few steps forward to be rewarded with a cut-scene after which you'll have to start a battle with two mutants (similar to Bane from one of the previous levels).