Before you is a well-known type of mission during which you will have to reach the assassin hideout by following the hints displayed on-screen. This time it won't be a full-time pointer, but an indicator showing your distance to the assassin #1. Luckily you don't have to hurry this time, as you're not limited by anything. In order to locate the assassin, you have to head to the north-east part of Arkham City, to the industrial district #2.
The place you're searching for is a big hole in the ground, the Subway Maintenance Access #1. It can be found in the western part of the industrial district #2.
As the four enemies found here are using firearms, it would be good to attack them by surprise. I'd suggest jumping down, carefully approaching them and taking down two of them at once #1. Afterwards quickly finish off the two others, without letting them damage Batman too much. Now you can jump into the large hole #2, reaching the Subway Maintenance Access.
Choose the tunnel heading north #1, overcoming a few small obstacles on your way. After reaching the crossroads turn left, to the west. Your goal is reaching the place from which you will see three Joker Thugs below you #2.
It of course would be good to attack them by surprise. Look out for the armoured enemy #1, first stun him with your cloak (B) and then lead out some quick attacks (X). Afterwards head west and turn north. Hold down the right trigger to walk below the partially raised gate #2.
You should reach a tunnel with a big abyss. Choose the Line Launcher, aim (left trigger) at the opposite wall #1 and shoot the line (right trigger) #2.
That's unfortunately not the end, as a standard use of the Launcher won't be enough. Once Batman starts moving along the line, hold down the left trigger to slow down his movements. Wait until you reach a branching, quickly turn the camera left and aim at the next (west) wall #1. Press the right trigger and Batman will automatically turn 90 degrees #2.
After safely landing on the proper ledge head south #1, walking below another partially raised gate on your way. Note the enemies below you and note a destructible part of the floor #2. Use the Explosive Gel to break through to the other side.
Blowing up the floor will of course alarm the thugs, so you won't be able to surprise them. Jump down and start attacking the inmates. Stay very cautious, as the small room makes it harder to dodge attacks than normally. Start off by attacking the enemies with firearms and knifes #1. It's also worth to blind the dazzle the enemies from time to time, either by using a Smoke Pellet or letting one of them throw a fire-extinguisher #2.
After you're done with them, take out the Cryptographic Sequencer and use it to hack into the nearby control panel #1. You will of course have to solve a mini-game to create a password #2, in result gaining access to the subway station.
You shouldn't encounter any enemies on the station, so start searching for an interactive door in the northern part #1. After crossing the narrow corridor you will reach a place where you will need to use once again the Line Launcher #2. Aim at the distant wall and shoot the line (this time you won't need to change the direction).
After reaching the new ledge, look up and use the Grapnel Gun to reach the higher level #1. Open the door leading to the Collapsed Street. Wait for Batman to regain his strength, head north and afterwards turn west to reach a new abyss #2.
Prepare the Line Launcher and aim at the opposite wall #1. Now you can act in one of two ways. The more obvious solution is allowing Batman to reach the next ledge, though I'd recommend changing the direction. Hold down the left trigger and wait until you get nearby the room with enemies #2.
If you decided to change direction, you will be able to surprise at least one of the enemies here #1. During the proper part of the fight, focus mainly on eliminating the inmates equipped with firearms or those planning on obtaining one #2.
Look out the armoured enemy, stun him before attacking. As the fight will take place beside an abyss, you can also try approaching the ledge and throwing enemies down #1. Hear out the conversation with Oracle and use the northern door #2 leading to Wonder Tower Foundations.
Inside the room you will face a new difficulty, a using the Detective Mode to trace enemy movement will be impossible at start #1. The only solution to this problem is locating the enemy with the jamming device, you can recognize hi m by the antenna sticking out of the equipment on his back #2.
In order to neutralize the thug mentioned above, move onto one of the vantage points on the left side #1. Wait for him to move away from his buddies and walk below the vantage point, so that you're able to use the well-known inverted takedown #2. After a successful action you of course have to quickly move away from the place, as Joker's men are also equipped with transmitters.
There are five enemies left to take care of and you can do it in any way you like. I'd suggest sticking with glide kicks #1 or using the grate on the lowest level on the room #2.
Unfortunately, just like before, you have to take into account that one of the enemies might at some point panic and take Fiona Wilson - the nurse - as hostage. In such case, quickly move to the nearest vantage point #1, wait for the enemy to turn around and QUICKLY jump down to attack him by surprise (Y) #2.
After you're done with the enemies, return onto the upper balconies and approach Fiona Wilson #1. Batman will transport the woman to a safe place and afterwards speak with her. Afterwards return to the main room and head north. You need to find the door leading to the Wonder Avenue #2.
Wait for Batman to pull it together and approach the first gate. Take out the Remote Electric Charge and use it on the engine sticking out of the ground #1. Ignore the inmate with a blade in his back, as he's only an announcement of what's waiting for you. Approach the second gate and use the Electrical Charge again to open it #2.
Right after going through the second gate, a group of assassins will surround Batman #1. Generally you fight them like the standard enemies with knives, though they're more agile. I'd suggest evading often (including those suggested by the game, used by leaning the analog stick and holding down Y) and jumping over the assassins #2.
After the fight is over, approach the third gate and turn on Detective Mode. It will let you see that the third engine is below a destructible floor fragment #1. Use the Explosive Gel and afterwards the Electrical Charge to set the engine in motion #2.
Now you can enter the main part of the Wonder Avenue #1. Head straight and soon you should reach a large gate #2. Listen out Batman's comment regarding analyzing one of the mechanical guardians, which should be helpful in establishing how the assassin you're tracking reached the next room.