Notice! Before attending this mission, I'd recommend you take a look at the mini-encyclopedia (Waynetech) which offers - inter alia - a description of all of Batman's gadgets and attacks at your disposition.
Now you can also access the map, thanks to which you will be able to locate your destination point more easily. You can do it by pressing the BACK button. Solomon Wayne Courthouse can be found north of your current location #1. The game doesn't require you to attend this mission at once, as the sandbox character of the game lets you spend any amount of time you like on finding secrets, fighting the bad guys and completing side missions. You are also completely free to choose your preferred way of reaching the courthouse. As a result, you can jump down and venture the streets of Arkham City, or follow the roofs. In the latter case, I'd suggest using gliding (by holding down A) #2 and the Grapnel Gun (RB), thanks to which you can easily grab onto the roof edges and other interactive objects.
The more obvious method of reaching the courthouse implies using the front door, though you will have to deal with the bandits standing there. It would be good to attack them from high above, aiming at one of them #1 and attacking (X) #2.
Start eliminating the enemies gathered around the courthouse #1. It's of course worth to enrich your combos with attacks described in the encyclopedia (and known from the first game) to gain more experience points. You can now head to the mentioned front door #2.
The less obvious option implies gliding onto the balcony above the main courthouse entrance #1. In order to make sure you'll reach it, you'd have to jump off one of the nearby taller buildings. The advantage of this method is that it lets you avoid the enemies gathered by the entrance. You'd have to eventually find a door in this case as well #2.