** Spoilers Ahead **
This achievement is for the last Riddler mission, finishing the "Enigma Conundrum" side-mission arc.
First off, before being able to do this last Riddler mission, you need to do the following things:
1. Finish the other 5 hostage missions before this one.
2. Obtain 400 of the available Riddles (can include Catwoman riddles).
Location:
After getting 400 riddles, the Ridder's location will be revealed. It is in the Bowery and not far from the Museum. Just north of the Museum, and all the way to the West wall, there is a square shaped section made so you can go under the overpass above. Down here, there is an electric fence, with a door off to the left. This is the location to the final hideout.
Walkthrough:
Inside, the door is rigged with bombs and you cannot enter through it. Above you is a grapple-able ledge with a vent. Go through it and you can see a general layout of how the test is set up. The Riddler is visible from the vent, and you can see that he has 8 people forced to walk in circles on the floor. If they stop moving, they will die, because he has placed explosives on their neck.
After dropping out of the vent, follow behind (but not too closely behind) one of the hostages as they walk the track. You will eventually come to a break in the wall, where you can stop for a second, before following the next track. There will be another break after making almost a full loop on this second track. This break will place you by the stairs that lead to the Riddler, where you can see that the floor under him is breakable. Following this third track around will put you under him, so you can do a takedown. Doing this ends the challenge.
Cutscene:
Batman puts the Riddler into one of the same devices he had the hostages in. He leaves the hostages there, with the controller the Riddler was holding. Riddler is forced to walk the track. You can now leave through the door which was armed with bombs before.
Side Notes:
It seems you don't really need gadgets at all for this test, as you do the entire thing on foot.
When trying to decide when to get in line behind a hostage to follow, know that between some there seems to be a larger gap. If that makes you more comfortable, go for it.
As for obtaining the 400 riddles required, I had video's posted here but they are no longer working. Unless someone tells me that posting their videos is ok, I won't go grabbing them. I can only suggest to look to Youtube if you are really having trouble.
You can also just find them by doing interrogations on inmates at various locations. If you go into detective mode, they should be highlighted green instead of blue or orange, and they appear green while in combat too. Just beat up the other inmates around them until the prompt shows up on screen at the bottom saying Y-Interrogate and Riddler secrets will be added to your map.