You will be able to approach this side mission after saving Vicki Vale, that is after completing the Rescue Vicki Vale from chopper crash site. Open the map and check out the Park Row area to find a new interactive point #1. After getting there, listen to a message from Alfred, who has apparently finished working on the cure and it would be good to try it out as soon as possible. Head to the marked point, a roof guarded by a few inmates #2.
The enemies on the roof will be using firearms, so it would be good to attack them by surprise and use gadgets to your advantage (especially smoke pellets #1). After the fight is over, land on the roof and take cure #2.
A very interesting cutscene will start, during which it will turn out that the Mad Hatter has tricked Batman #1. After the cinematic ends, start tapping A #2.
It's not the end however, as in order to "break out", you will have to fight with a very numerous group of enemies #1. During the battle, it will be very important to use counters often #2, as Batman will be almost constantly surrounded by a numerous group of enemies.
Keep looking for the Mad Hatter, who will be appearing from time to time #1. When he does, ignore the normal enemies and focus on attacking him. During one of such attacks, you will be able to finish him off by pressing the right trigger and Y at the same time #2.
Doing so will lead to defeating the Mad Hatter #1 and ending the whole mission. You will be able to use the door to get out of the building #2 and return to Park Row.