Most Wanted: Two Faced Bandit
Note: First location shows up automatically
Objective: Stop Two-Face and his men from robbing Gotham's banks
After hearing the details about a bank robbery about to happen on Bleake Island, burn rubber across town to arrive at the front doors. Stroll inside (yes, Batman actually uses the front door for once. I was in shock too) tor trigger a scene showing Harvey's men arriving and starting their withdrawal.
After the scene ends, Batman will mention that the blaring alarm you can hear will prevent Two-Face's goons from hearing you. This allows you to be a bit more open with your attacks and finishers, but remember that it doesn't affect their eyesight so you still need to be cautious. At the top of the screen, the bar with a money value underneath shows how much time/ money is remaining until Harvey's men get away and blow the joint (killing you).
Also of note is the counter to the right of the bar that shows how many thugs you need to bring down to enter the second phase of the heist. Now that you've taken all that in, it's time to go to work. The floorplan of each bank is different, as well as the objects and grapple points that you can interact with. Two things to remember are to use inverted takedowns (from a high point) and silent takedowns from a duct underneath the floor when you can.
Note: If a thug sees you use a duct grate, they will lob a grenade inside which seals it.
These are quick and generally allow you to take out the thugs unseen (inverted especially). You'll see how effective the inverted takedown is if you watch the video for the third heist as nearly all of the 15 thugs were taken down with it. In the first bank though, you have a fair amount of time and you only need to deal with 8 thugs before the money bar is depleted. Death will return you to the start of the robbery, so you won't lose much progress here. Use this early heist to get the feel for what you can do/.interact with and how to seperate the thugs as the later heists are more challenging.
When you reach your quota of sleeping thugs, the money bar and counter will vanish, signifying the start of phase 2. Two-Face will deactivate the alarm, returning the thugs hearing to normal. For this phase you have no time limit. A checkpoint also triggers when this phase begins, so you won't start the robbery over (breathe a sigh of relief). So take your time, watch and single out thugs and use the environment to your advantage if you can. It's essentially business as usual for Batman gameplay.
Once all the remaining thugs are taken care of, you'll have a brief chat. The front doors of the bank will open and you'll be free to leave. Apparently Two-Face isn't happy about your little 'interruption' and is planning to rob the bank on Founder's Island next.
The Founder's Island bank has a more difficult layout for effective attacks. This is due to to the large open central area which offers the thugs a decent line of sight. You will need to take advantage of the upper areas of the bank (second floor) and/ or the duct system to make things a bit easier.
There are ten of Two-Face's men to bring down before you enter the second phase for this bank and the money will vanish a bit faster as there are more crooks moving it. Overall this one requires more stealth an subtlety than the previous one to emerge victorious. But if you use your surroundings well and time your attacks properly you should make it through safely.
The third and final bank is of course the hardest of all (although the layout is slightly more forgiving than the second bank). This time you will need to take out fifteen thugs in phase one and deal with them having two drop points for the money (meaning the bar depletes fairly rapidly). You will need to use all your skills and use the environment well to even have a chance of getting through this in time. Or you could just do what I did and use repeated inverted takedowns to create a pile fifteen goons high next to one of the money drop points. Stealthy? Not so much.
Phase two is where you finally get to confront Two-Face, who is now sufficiently pissed off at Batman to show up in person. Harvey is wielding a shotgun, making a direct assault on him almost impossible. Flanking him are four thugs wearing optical camoflague (making them difficult to see in detective vision) and a detector thug who will slowly pinpoint your position if you use detective vision too much. The best way of bringing Two-Face to justice is to use the ducts under the floor to initiate a Fear takedown (watch the video for a 5x Fear takedown).
Once that is over, you'll need to bundle up Harvey and deliver him to GCPD lockup. Job done.