Explore the yard where you have just fought and find the manhole separating this location from the sewers [Blackgate - Sewers Access]. Follow the linear corridors and reach the place where it will be necessary to detonate the floor with the explosive gel. Jump into the hole and, after you land at the bottom of the shaft, look up and locate the interactive ledge that you can use the hook on.
Go North, use the grapple along your way to extend the rope. Walk over the rope and reach a new area with discharges. You need to use the grapple twice here, each time to extend another rope and walk over it onto the neighboring platform. Climb onto the ledge above and walk along the narrow corridor to reach the area where you need to use, again, the explosive gel. After you have done that, glide towards a more distant ledge with the murdered guards on.
Approach the power supply device and press the appropriate key/button to sabotage it, which will lead to the disappearance of the discharges. You can now approach the water and create a floating platform, using a glue grenade. Jump onto the raft and start moving, by using the claw on the successive anchor points. After you have sufficiently neared another ledge, use the hook on the balustrade.
Enter the control room and press the button to make discharges appear in the distance. You now need to select quickly the remote controlled batarang from the inventory and throw it there, which will charge it (if you do not manage to do it in time, press the button again) Right after the batarangs charges, send it towards the fuse box on the left (the screenshot).
Note that the destruction of the fuse box caused the water level to rise. Return to the previous area and in the way that you have already earned (glue grenade) create a floating platform. Jump onto the platform, pull yourself towards the anchor point, using the claw and spread the explosive gel onto the wall here to destroy it. Climb onto the ledge, go ahead and stuff both holes with glue grenades.
Look down and use glue grenades on the two pipes that you can see in the distance. Only after the process of leaking steam stops, create a new platform onto which you need to jump down. Note that the platform starts moving on its own and you will have to plug the holes in the pipes along the way. Start with the pipe shown in the screenshot and, just as quickly, duck to prevent being pushed off the platform.
Aim the glue grenades at two other pipes (they are located on the right). Finally, send the glue grenades towards the three pipes above shown in the screenshot. Note - you need to do that before the platform that you are currently standing on, is destroyed by the whirling blades so, be quick about it. Once you have finally stopped the leaking steam, use the hook to reach another ledge above. You can now go through the door to the Prisoner Processing room.
There are four inmates in the room where, if you hurry, and do everything correctly, you can eliminate two of them with a single surprise attack. After you have dealt with the other two, use the shock gloves to charge the local generator. Wait until the elevator arrives, climb onto its top and use the hook to reach the top of the shaft. Take the door to the prison's main area [Nexus].