You start in the Control Room. Locate the interactive ledge above and use the hook to get onto it. Walk through the venting shaft and reach the area with the Death Rows. Find a hole in the fence and jump down to a lower level of the cell block, where you will watch a cutscene.
Start a new fight, during which you will be able to count on support from Captain Gordon. Just like usually, watch out for the martial artists and do not allow them to land too many blows. After you have charged the shock gloves deal with the enemies with shields, who are not going to be that demanding anymore.
[New character trophy: Warden Joseph]
Go east and leave the location with Gordon and Joseph [Execution Chamber Access]. Turn to the South-East, and open the door to the Prison Chapel. You can now approach Joker, which will result in another cutscene.
Be prepared to press the counter-attack key/button and stat landing the standard blows. Perform further counter-attack and start tapping rhythmically on the attack key/button, which will result in defeating Joker.
[New Batman Suit] (you can put it on after you return to the Batcave)
Note - After you watch all of the final cutscenes, you will return to the main map. Depending on your preferences, you can either continue the game and focus on all of the side-activities, or start the game again on a higher difficulty level, by choosing the New Game Plus mode.