Walk forward, still following the homing beacon, to trigger a cutscene. You then have to find the secret entrance to Wonder City. Unfortunately, even though the entrance is in the same spot every time, you still have to scan for data on its location.
Scattered around the map are seven Mechanical Guardians: four on the ground floor, three in the top floors of apartment buildings. There are also two fights against a pair of Assassins. The Guardians are all easily locatable by using Detective Mode. When near them, hold down the Scan button to collect data about the entrance.
Once you've collected all the data, the secret entrance will become available. It's hidden in the wall immediately to the left of the large door blocking your way earlier. An Assassin will come out of nowhere as you investigate; Counter her to take her sword and use it to fit into the lock.
Go through the door and head right. Climb up a ladder and a manhole, and Batman will hover near death once again. This time, once you have control, you can only move slowly. Just keep walking forward.
Chamber of the Demon
This section is mostly story-driven. Just keep walking forward and follow Talia al-Ghul to the location of your first Demon Trial.
All you have to do for the first trial is drink from the cup. It will restore your health and all your combat abilities.
For the second trial, you need to follow the spirit of Ra's al-Ghul through the newly-created wasteland. You are only allowed to touch the blue, icicle-like platforms onto which you can Grapnel. These will serve as your checkpoints. This is the first time you'll need to really get used to the momentum properties of your Dive Bomb. The simplest way is to follow the trail. Reach the first checkpoint and listen to Ra's' speech. The second phase of the trial requires you to do shorter Dive Bombs. When you grapple up to the next checkpoint, get ready to fight some more ninjas, before your third Dive Bomb challenge awaits. Instead of Grapneling onto a platform, you need to Dive Bomb into the large sandstorm.
The fourth Dive Bomb challenge is much trickier, as there are several beams making the flight path much narrower than before. Use your Dive Bomb sparingly and instead focus on navigating between the beams, while Dive Bombing whenever you have space. The fifth challenge is similar, and when you reach the checkpoint platform you'll have more ninjas to fight. One final sandstorm challenge awaits, and your second trial will be complete.
Run up the stairs and talk to Talia al-Ghul, and she will let you go through to the next room.
BOSS FIGHT: Ra's al-Ghul
You will be transported into a sandstorm similar to the Wasteland in the second trial. After a few moments, Ra's will charge at you with his sword. Dodge him, and then Ra's will spawn more ninjas to fight alongside him. This fight works similar to the final wave of the fight against Poison Ivy in Catwoman's story; most of the time you will be fighting the ninjas but every so often Ra's himself will deliver a powerful attack which you need to dodge.
After one wave of this, Ra's will summon a gigantic version of himself, protected by a circle of ninjas who rotate around him. There are a number of sizeable gaps in the protective wall where you can quick-fire the Remote Electrical Charge to damage Ra's. Ra's will also throw ninja stars and send massive blades your way.
Once you've done enough damage to Ra's, he will return to his human form and leap at you with a flurry of attacks. Mash the Counter button to block him, and after a while you'll trigger a short cutscene, after which the second part of the fight begins.
A swarm of ninjas will leap towards you, all of them with Counter symbols over there heads. Tap the Counter button furiously to swat away as many as you can, and then continue the fight just like the first phase. When Ra's returns to his larger form, he will have stronger, faster attacks, and the ninja wall will have only one small hole through which you can attack. Be patient and time your quick-firing to compensate for the speed of the wall.
Ra's will do his Counter flurry one more time, and then it's time for you to Beat Down him back. You're almost there...
After a short cutscene, Ra's will take Talia hostage, and Batman activates the Reverse Batarang. Use it to hit Ra's in the back of the head before he kills Talia.
Manufacture The Cure
Run forward and drop into the sewer again. Backtrack through the Wonder Tower Foundations and into the Subway Terminals. The now-familiar abandoned subway cars will give you a new Predator section. This group of enemies are all wearing thermal goggles, and one of them has a radio jammer. As usual, take out the jammer first; this time, however, you'll want to keep moving to avoid being spotted by the thermal goggle thugs. Pop in and out of gargoyle cover, quickly taking out one thug at a time before retreating.
Once you've cleared the room, head toward the west exit into the Subway Tunnels.
Another forced fight here introduces you to Riot Shield users, who will block all frontal attacks. There are two ways to deal with them, an Aerial Attack (Stun + Stun + Jump) or one of your Special Combos. Either way, make sure you take them out quickly so you can deal with the rest of the enemies without any trouble. Continue to move towards the surface, and you'll hear a group of enemies. Take them out, and be sure to relentlessly use your Special Combos to deal with the tougher enemies. When they're finished, use the Cryptographic Sequencer on the console in this room to reach The Bowery.
Interrogate the Mayor
Once you've reached The Bowery, there will be another Oracle conversation about Mayor Sharp, and your objective marker will change. The Mayor will be surrounded by five armed thugs. Beat them up and walk up to the Mayor to interrogate him.
You'll then need to head back to the GCPD building to complete this part of the game. Joker has set up a handful of snipers whom you need to take out, at least on the harder difficulty levels (if playing on Easy, you might be able to avoid or take their fire without much trouble).
When you've dealt with the snipers, your next big fight is right in front of where you entered the GCPD building last time. Now there are four regular thugs, an armoured thug, and two riot shield thugs. Get the drop on one of the riot-shield users first and take him out. Keep in mind that at this point thugs can pick up dropped weapons (there's a Special Combo to destroy weapons you can get later), so get rid of the two riot shield users then beat up the regular thugs before they can pick up the shields themselves. Save the armoured thug for last. Once everyone's dealt with, use the Remote Electrical Charge on the shutter the thugs were guarding, and head inside the GCPD building.