Identity Theft

Identity Theft is a Gotham's Most Wanted Side Mission in Batman: Arkham City.

Description
"'Find out who is behind the Identity Theft murders.'"

Walkthrough
The Mission in unlocked once Batman enters the Bowery district after escaping the old GCPD building in the Amusement Mile.

First Victim
The body can be found directly east of the Museum and the Subway entrance in the Bowery. Investigating the bandaged head reveals that the victim's face was removed via highly-precise surgery. This manner is similar to a string of recent murders with similar circumstances. Scanning the blood splatter next to the body determines it is the victim's blood and can be used to find the one responsible or perhaps a witness. The trail winds through the streets to the southeast corner of the district where a cowering prisoner is in a small alley.

Confronting him reveals that he did see the murder take place, but shockingly the murderer's face resembled Bruce Wayne. With nothing else to go on for now, the investigation stalls.

Second Victim
After dealing with the events in the Museum, Batman can find a second body propped against a wall in an alley north of the Monarch Theatre. Investigating the head again reveals details on the killer's M.O. such as paralyzing the vocal cords to prevent screaming. It also demonstrates the advanced degree of planning required for such a kill. Scanning the surgical scalpel next to the body brings up a fingerprint that, to both Batman's and Oracle's shock, comes up as a near match for Wayne's.

Oracle attempts to rationalize how Bruce Wayne's fingerprints turned up at a murder, perhaps a result of the repeated exposure he took from Scarecrow's Fear Toxin during the Asylum takeover, or Hugo Strange accomplishing implanting a post-hypnotic suggestion when Bruce Wayne was arrested and brought in. Both are entirely uncertain of what is a suitable explanation except to keep looking for more bodies and hope evidence turns up.

Third Victim
A third body can be discovered in a small courtyard immediately adjacent to and southeast of the Ace Chemicals building. Investigating the crime's focal point shows that the removal process occurred prior to the victim's death and carries an indication that the killer places a priority on what is collected over what is left behind. Scanning a chemical residue next to the victim's foot reveals someone used bleach in an attempt to clean up the mess of the murder, yet in doing so left an entirely different trail for Batman to follow.

Following the trail through a few inmate-heavy areas eventually leads to a lone inmate hunched over a gutter running with water, two bottles of bleach nearby as he tries to wash his hands of the stuff. Batman interrupts the cleanup to interrogate him and learns that he was ordered by Bruce Wayne to get rid of the body and use the bleach to cover it up. Further prodding uncovers the Killionaire's location at an apartment near the Courthouse.

Identity Thief's Hideout
Going to Park Row and moving through the alleyways behind Two-Face's former base leads to the mentioned apartment. Inside, amidst scattered news articles about the murders and a hardly-sanitary medical setup, Batman finds an audio journal that exposes the identity of the Identity Thief: the renowned surgeon Dr. Thomas Elliot. Just as the journal ends, the devil himself appears behind a shutter trapping Batman in the room. Eliott mocks the Dark Knight before presenting his masterpiece under a 'mask' of bandages: an almost-perfect reconstruction of Bruce Wayne's likeness minus some scarring that will fade with time.

With his final taunt, he leaves Batman to deal with the turmoil present in Arkham City while vaguely threatening further trouble to come in the equally replicated voice of Wayne.

Once freed from the cage, Batman laments Eliott's escape with the promise to continue his chase for the homicidal maniac once his work there was finished. The Missions ends.

Trivia

 * Despite the presence of a bio on him in Arkham Asylum that indicates they had interacted prior to Joker's takeover of Arkham Island, this mission retcons the history of Hush in the Arkhamverse so that they met for the first time in Arkham City. This is because the first game wasn't planned to have a sequel and there was no way to explain in-universe how Batman did not immediately suspect Elliot of the crimes until he revealed himself.