Note! Before you start this mission, consider starting the Enigma side-mission, thanks to which you will be able to take care of the actions connected with it, on a regular basis. Apart from that, I recommend that you find some spare time to take the journey back to the Batcave, to talk to Alfred about Enigma and gain the valuable experience.
The arms dealer that you are looking for is staying at the same location as previously, i.e. in The Bowery district. the problem is that the fast-travel point in your destination is currently inactive at the moment so, you will have to take a pretty long journey across the major part of Arkham. If you want to take to this mission straight away, you will probably start in the South-Eastern district [Coventry]. In this situation, set out to the North and go over the Gotham Pioneers Bridge.
Further along your path, you will have to walk around the Sheldon Park district from the Eastern, and then from the Northern side. Towards the end turn West. Your destination is the alley shown in the above screenshot, which you can get into by flying through the hole in the glass roof. Watch a cutscene here of the Loose Lips dealer dressed up as a Santa Claus, as well as a few characters hostile towards Batman.
After you have regained control over your character, bounce off the edge and start falling. On your way down, try to aim at one of the bandits and eliminate him right at the outset. After you start the fights, eliminate the enemies one after another, while remembering about the cape swipe in the case of the armored enemies. Leave the dealer for the very end. Grab him and conduct a quite violent interrogation, thanks to which you will obtain a SIM Card and determine how you can locate the Penguin. .
[New Character Trophy: Gotham criminals]