Forcing the Mercy of the Court
Basically there are a few ways you can drop in, but they all result in the CS in which you help Catwoman rescue herself -- and then chat her up to learn what she knows. Just as things start to get interesting, Joker tries to snip the Cat -- and after she departs you unlock the Achievement "Acid Bath" (10 GS) and receive the new objective to find and interrogate The Joker. Well yeah!
Rescuing the Catwoman
Tap LB to open the Detector Unit and scan the bullet hole in the window, and then the bullet strike point to gain the trajectory -- which you are shown. Now here is the thing -- if you want you can go directly to that building -- but this is also the first opportunity that you have to meet up with the Mysterious Watcher -- and I know you want to do that!
So use the Grapnel to go up and get back on the wire, retrace your steps to the other side, and then exit the building on the second floor level through the door on the right hall (facing towards the front of the Courthouse). Outside you are on the balcony and you overhear the conversation of the hoods below -- who want nothing to do with you which is why they are keeping the door locked!