Before leaving the area, you can have an optional conversation with Two-Face. He's hanging at the same spot where Catwoman previously was. As for choosing the exit, you have two options. The more obvious solution is using the Grapnel Gun on one of the upper floor windows #1. It would let you reach the previously examines balcony #2 and from there to one of the exits.
If you don't want to follow the same route, you can head to the door located in the corner of the room #1. A few moments later you will reach a rear entrance from the courthouse #2.
Notice! If you have left the building through the front door, be ready for eliminating some more enemies!
You next target is the Medical Center found inside the church located north-east you're your current location. Depending on your taste, you can get there by following the streets #1 or gliding #2 and using the Grapnel Gun.
Regardless of the chosen method, you have to reach the Medical Center entrance. It would be good to surprise the enemies gathered there with an attack from above #1, though it's not absolutely essential. Of course remember to make use of counterattacks and dodges throughout the fight #2.
Once you're ready, use the door leading to the Medical Center #1. After getting inside, go to the next room and be ready to quickly press Y when Harley Quinn attacks #2. Listen out the short conversation with this character, after which Harley will exit the building and leave you with a few armed enemies.
Now you have to perform all the moves flawlessly, or else Batman ore one of the hostages is going to die. Start off by pressing Y to throw a Smoke Pellet #1. Afterwards QUICKLY press RB so that Batman uses the Grapnel Gun to get onto the gargoyle statue #2, getting out of the enemy's sight.
Follow Batman's suggestion and turn on the Detective Mode #1. That way you will learn that there are four armed enemies in the building and two of them have taken hostages. Eliminating them will be very linear, though the game won't leave any place for mistakes. Start jumping through the gargoyles #2 using the Grapnel Gun (RB).
Stop after reaching the second vantage points and Batman will notice the enemy with a hostage below #1. Hold down A and start gliding towards him #2.
After reaching the balcony above the enemy, press Y to take him out #1. You need to hurry, as otherwise he will kill the hostage. Afterwards you can use the Grapnel Gun to return onto the nearest vantage point #2.
Now we will focus on eliminating the second guard with a hostage #1. Move to the vantage points closest to him and afterwards glide down #2, landing behind them.
Crouch and approach the destructible wall #1, beside which the guard is standing. In accordance with the received instructions, press Y to break through the wall and take down the bandit #2. Once again return onto the gargoyles.
Now you need to eliminate the two last enemies, who should now be standing beside each other #1. Move to one of the neighbouring ledges and press B, making Batman quietly land behind their backs #2.
Press and hold the right trigger and approach the guards. Make sure that you're standing close enough and press Y #1 to perform a double takedown. Afterwards you can take a look around the medical center without being disturbed by anyone. I'd suggest talking with the doctors, Adam Hamasaki, Anne Bishop and Aaron Cash #2.
Head towards the door left of the Medical Center exit, in the north part of the building #1. Go up the stairs onto the upper platform and use the Grapnel Gun on the ledge visible in the distance #2, thanks to which you will be able to continue the climbing.
As the stairs to the bell tower have been damaged, keep using the Grapnel Gun to grab onto the upper ledges #1. Eventually you should reach the ladder leading into the bell room. After reaching it, approach the sniper rifle from which the fire has been shot #2.