This introductionary sequence will show Joker after he's been recaptured by Batman. The madman is being transported back to his cell and all you're allowed to do at this moment is to move around. The only exception is the screen zoom function and you might want to try it out if you can't see Joker's face clearly from the normal perspective. You'll have to wait for Joker to break free in order to gain access to Batman's other moves.
You start the game in an area called Holding Cells (use your personal map for navigation) and your first objective will be to defeat two groups of thugs. Thankfully both fights are going to be extremely easy. Notice that you can combine your punches to create combinations of hits. It would also be a good idea to practice counterattacks. You can perform a successful counterattack each time you've noticed that a blue icon has appeared over the head of one of your opponents.
Once you've defeated the first group you'll have a few seconds to prepare to for an arrival of the second group. The basic structure remains the same, however you can also practice stunning thugs with your cape and performing takedowns. Each time you begin a new fight try scoring good combos, so you'll earn more experience points. Joker will unlock a new passageway once you've dealt with his men.
Head north and you'll soon arrive in the Processing Corridor. Keep going straight until you encounter two thugs. Getting rid of them should be a piece of cake. You can now turn left and find Eddie Burlow. If you don't want to talk to him (it's not mandatory) proceed to your right without any further delays.
Turn left in a short while and go to the area marked as the Patient Pacification Chamber. It would be a good idea to talk to Zach Franklin here (one of the guards) and you'll find out that an inmate called Zsasz is holding his colleague hostage. Ignore the left corridor and instead proceed north. Locate a small staircase and proceed to the upper floor where you'll be allowed to talk to Gretchen Whistler.
Head on to a nearby balcony. You'll come across new guards here and you'll be allowed to talk to one of them. Go left once the conversation has ended, turn on your detective mode and look up. Press a corresponding key to grapple up to one of the gargoyles. Thankfully it's all going to be performed automatically, so you won't have to worry about losing balance. Use the hook again to reach other gargoyles located in the vicinity of your character.
Eventually you'll end up on a gargoyle on the side of the room. If you look down you should notice that you're stationed directly behind Zsasz. You must now perform an action called a Glide Kick. This is also triggered by pressing a single key and all you have to do is to what for a large icon to appear above Zsasz's head. Once you've stunned your opponent perform a quick takedown to finish him-off.
Activate detective mode again and inspect the northern wall of the room. Doing this should allow you to locate a new entrance to a ventilation shaft. Use the tunnel and kick a new grate at the opposite end. You'll end up standing in the Processing Corridor. Head straight and you'll soon arrive in an area called Decontamination.
Approach one of the guards. You may take your time to see what's happening on the other side of the glass. Sadly you won't be allowed to rescue those guards. Don't worry, because other allies are still alive and you'll reach their positions in a short while. Look up and grapple up to a higher ledge. You must enter a new ventilation shaft here.
Exit the vents, turn right and rescue the first guard before he loses grip and falls. If you arrive too late consider returning to the last checkpoint, because you ought to rescue everyone. Stand in the middle of the platform and HOLD the run key. Doing this will allow Batman to perform a jump automatically once he's close enough to the ledge. Make a few steps forward and look around.
You'll now have to use your hook to grapple up to a higher platform. Once you're there turn left and rescue a second guard. You'll now have to glide to a nearby platform seen in the distance. The idea here stays the same - press and hold one of the action keys and Batman will automatically begin gliding once he's close enough to the ledge. You can also make small adjustments while still in flight, but it shouldn't be necessary.