Wow, you know what I call this? Awesomeness. :P

The method I used was, right at the start, swing across to the opposite gargoyle. Drop down, spray explosive gel on the concrete wall. If no one has seen you yet, drop into the grate, and go left or right. If no one is alerted they will be walking calmy and you can get the vent ko from the guy who walks right up to the vent.
Next return to center (by the gel) hug a corner next to your prepped wall. Throw a sonic batarang behind you, under the gargoyle. (without leaving your cover) When someone comes to disable it you get your corner takedown.
Quickly drop back into the grate before anyone shows up and wait. When someone comes to inspect the cronered guy, detonate the wall, there's you gel takedown.
As everyone goes to inspect the explosion, go out the vent you previously used for the takedown. Head back to the gargoyle you started the room on and after a brief wait you should have a setup for the hanging one.

Ha! I actually used this room to try to complete this challenge. It didn't work for me but I see now that I misunderstood what they meant by hanging ledge takedown.

yeah did u

Do you have to defeat Copperhead before the helicopter casefile triggers?
Because I'm playing I am the Night mode, and can't go back to the rooms and have people in them in New Game Plus, or the normal game. Copperhead would likely kill me, and I don't really want to go all the way back to the beginning just to get a sonic batarang upgrade.

what if you did themost wanted thing before you get up to part 6?

its great

does this have to be in roam or can you unlock this in challange mode

Soory but it would be a bit too much..there are many tricks that require waiting and it would be stupid for video..i can tell you some tricks..but to win achivement you need to search youtube..i just show one of more difficult task

gener@L chet! can you make video how to win achivement: Thanks, old friend! ??