take the door to the corridor with holding cells [Block A Holding Cells], and pay attention at the same time to the reconnaissance drone flying by. Soon after you take a turn to the right, the game will automatically, start another fight, where you will have to beat up the inmates released from the cells on the sides. Deal with all of the prisoners, who fortunately will not be too much of a challenge. After you have dealt with them, follow the game's suggestion and use the hook (Grapple) to reach the narrow passage underneath the ceiling.
Jump down and take the door to the next area in the prison [Nexus]. Here, you will have to deal with an armored enemy for the first time, whose eliminating is a bit more tricky. you need to swipe your cape first (the above screenshot), which will temporarily stun the enemy. Only after you perform that, lunch the attack by landing quick standard blows, which will result in the elimination of the criminal.
Go ahead and use the hook again to walk around another locked passage and reach the Prisoner Processing room. It is a good idea to activate the Detective Vision here, because this will allow you to figure out what the current situation is. Select from your inventory, the batarangs, initiate the targeting mode and target the button shown in the above screenshot.
You might have already noticed that the gate rose just a bit. Run up and press the trigger/key suggested by the game, right in front of the gate. Thanks to this, Batman will perform a slide. After you have eliminated the enemies, turn your attention to Vicki Vale held in one of the side cells, and interact with the new button (this time you do not need to use the batarangs).
[New Character Profile: Vicki Vale]
Enter the inactive elevator shaft and select the Explosive Gel from the inventory. Use the gel onto the unstable fragment of the floor and detonate it. Thanks to this, you will walk into the area with Death Rows. After you watch a cutscene featuring the Black Mask and Killer Croc stop at the grate of the venting shaft on the left and rip it out (by tapping on the action key/button rhythmically).
After you have left the shaft, land onto one of the prisoners and start fighting again. This one is nothing out of ordinary, although you can make it slightly easier for yourself by hitting the fire extinguisher with the batarang, which will temporarily blind the enemies. After you have dealt with the criminals, take the passage to the right of the grate with one of the gangsters. Select from the inventory the Batclaw here and use it to rip another grate out, and enter the venting shaft.
Run towards the wall, thanks to which Batman will automatically leap towards the shaft's entrance. After you end up in a small corridor, approach the severed fragment of the wall and spread the explosive gel. Detonate the charge, which will kill the gangster at the other side of the wall. You can now take the door to the area neighboring the Execution Chamber.
[New Character Trophy: Mobster]
Stop in the spot shown in the above screenshot, i.e. in front of the locked gate. You now need to solve an easy puzzle that consists in hitting the button on the left and on the right, of the gate, simultaneously. You need to do that by using the option of quick throwing of batarangs, i.e. by skipping the process of targeting. Double tap the targeting trigger/key, thanks to which Batman will throw batarangs towards both of the buttons and thus unlock access to the neighboring room.
In the already learned way, use the claw on the grate under the ceiling and reach the shaft. Walk through the shaft to reach the
Execution Chamber after several moments, which will start a cutscene of Commissioner Loeb, Black Mask and Killer Croc. Stand in front of the one-way window and take a leap towards it. This will enable Batman to ram through it over to the other side.
[New Character Profile: Calendar Man]