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Credit: Batman Arkham Videos
After you put on your batsuit, you are required to hack into their communications. After doing so, you will hear of Catwoman's appearance in Harvey Dent's Courthouse. You know that Catwoman (Selina Kyle) knows a lot about Arkham City already so you decide to go for her. At the front, there are goons, just knock them all out, once you have done that, enter the courthouse. In front of you are stairs, turn left on the stairs and then take a sharp right and you should receive a cutscene. Once the cutscene is finished, walk across the corridor and climb up the ladder. You should spot an armed goon on the balcony, watching the room, take him out with a silent takedown. Jump down from the rope and Harvey will have seen you, now take down all of the inmates or thugs that are willing to fight you. As soon as you finish the last enemy, you purposely get shot, and a cutscene appears. After the cutscene, you get the steam achievement.