Right at the start, you're given a simple crime scene. The only piece of evidence, the assassin's blood, is right at your feet. You won't be able to leave the room until you've scanned it, even though we won't technically be following the blood trail in this video. Once it's scanned, you'll have a short conversation with Oracle. Head upstairs and out the door.
Walk forward a few paces and you'll trigger another short conversation with Alfred, requesting the Line Launcher. At this point, the game wants you to follow the blood trail left by the assassin. Lucky for you, it's entirely possible to just run straight to the end of the trail without having to follow anything. Go to the waypoint as shown in the video, which is exactly where the blood trail ends.
Once you've hit the waypoint (the blood trail ends just west of the Ace Chemicals Building), you'll need to scan the next blood sample to collect more evidence. Scan it, but you'll never get the chance to complete it, as a female ninja smacks Batman in the back of the head. The chase is on!
Plant the Tracking Device
Follow that ninja through an obstacle course. It's not too hard, and because the game generously gave you a checkpoint, you can just select Restart if you make a wrong turn. Keep following her until you have her cornered on a rooftop. You don't want to directly fight her; instead, when she has the blue notifier over her head, press the Counter button and Batman will place a tracking bug on her shoulder. Batman then surrenders as per the cutscene, and Robin jumps in to save the day. He also gives you the Line Launcher.
Follow the Homing Beacon
We're still in Park Row, but not for long. Follow the homing tracker to the Subway Maintenance Access manhole in Amusement Mile. There are four armed thugs guarding the manhole. Don't even try to fight them; you can even avoid taking any damage by simply dive-bombing straight into the hole, just like in the video.
Subway Maintenance Access
As soon as Batman touches down in what for all intents and purposes is the obligatory sewer level, you'll trigger another short Oracle conversation. When you see some Joker Teeth, turn left, and drop down into a three-on-one fight against two regular thugs and an armoured thug. Take out one of the regular thugs when dropping down, then deal with the other so you can Beat Down the armoured thug in peace. Turn around and head right, underneath a gate. You'll now need to use the Line Launcher for the first time. It works the same as in Arkham Asylum, except now you can deploy a second line launcher by holding down LT/L2, aiming, and firing. You'll need to do this in order to get to the next area. Once you have your first Line Launcher going, look left and aim a second line launcher, then proceed forward.
When prompted, do a Wood Takedown to drop down to the bottom floor. You'll now have to fight against a good eight or nine opponents at once. It's nothing too difficult, except that on occasion, an unarmed thug will try to grab a weapon from one of two stashes in the room. You'll hear a loud klaxon sound when they try to grab a gun, so knock them out before they get the chance. If you can keep your combo up, there's no reason why you can't get a good 45x combo out of this fight.
Once everyone's incapacitated, use your Cryptographic Sequencer on the console near the fire extinguisher and NO ENTRY sign. The two large doors will open, and you'll be back in the area with the abandoned subway cars where you deactivated the last of Penguin's disruptors. The door you want is on your immediate right, just after Hugo Strange announces that Protocol Ten will commence in five hours.
Head left, then right, towards a water chasm. Use the Line Launcher to cross it, then reach the upper level with your Grapnel and head through the door.
Take a few steps forward and Batman will start convulsing and nearly die. Once you're back in control, run forward then left and you'll hear some thugs discussing the high-tech weapons they got from Joker. There are two ways to start this fight: either use a second Line Launcher to knock everyone down (maybe doing a Line Launcher Takedown too), or simply go around to the right and start beating them down properly. It's your choice. Either way, this is a mandatory fight that's not too difficult if you put your mind to it. In the video, I had some sort of glitch where the armoured thug disappeared into the water below, but don't count on being so lucky in your playthrough. Make sure you disarm the two armed guards first, then just keep countering and using Critical Strikes, and be sure not to accidentally hit an armoured thug mid-combo, otherwise you'll lose said combo.
Once everyone's down, you'll have another Oracle conversation, then it's time to open the door for your next big Predator section.
Wonder Tower Foundations
This is the first really challenging Predator room in a while, and introduces two new concepts. Firstly, one of the guards is carrying radio equipment that will interfere with your Detective Mode until you take him out. Secondly, the guard next to the intern Fiona Wilson will sometimes take her hostage, requiring you to take him out without being seen; if you're caught, the thug will kill Fiona and it's game over.
The key to this room is patience. As you step onto the first gargoyle, there should be a guard a little below you and to your right. Take him out and wait. A few more guards should investigate, and one of them is the radio man. After a few minutes, the guards will split up, then take out the radio man so you can use your Detective Mode properly. Now it's just an issue of cautiously and carefully taking out each guard one by one. You cannot afford to be seen here. If Fiona ends up being taken hostage, either use a Remote Controlled Batarang to knock out the thug holding her up, or sneak up behind him and use a Silent Takedown.
Once the room is clear, talk to Fiona to rescue her, and you'll trigger a short cutscene. Head back down to the bottom floor of Wonder Tower Foundations and go through the door with the Wonder City banner over it.
You'll trigger another Batman-almost-dies cutscene, then continue forward. Use the Remote Electrical Charge to power the battery on the floor, which will open the doors ahead of you. Walk forward and three Ninja Assassins will attack. Beat them up, then look for the next door battery. There's something covering it at first, which you'll need to detonate with the Explosive Gel, then walk through the door.