This is story-related and cannot be missed.
Once you enter the Patient Pacification Chamber and talk to Zach Franklin, a cutscene will appear of Victor Zsasz threatening to press the button to electrocute an unfortunate guard. After the cutscene, go up the stairs in front of you and approach a guard on the second floor to go through a bit of dialogue. It should tell you how to use detective mode and how to grapple up to a gargoyle. When you are at the back of the room, glide kick Victor Zsasz temporarily and then use a ground takedown to finish him off. A trophy added to the collection.