Killinger Department Store

Killinger Department Store, also known as Militia HQ or Arkham Knight's HQ, was an abandoned shopping mall located on Founders' Island. It was one of the buildings located on the old Gotham ruins, below the newer constructed buildings on the island.

Before Arkham Knight Incident
The department store was split into two locations (a North and South branch), but was eventually abandoned by the time reconstruction of Founders' Island began. Based on the conditions on the shops (decrepit, but not entirely vacated), the mall was likely closed in a short period of time.

It appears that both buildings were bought by CitiVision Construction for Founders' Island's reconstruction. While the south branch appears largely untouched, the north branch was converted into a massive ventilation shaft.

While preparing for the assault on Gotham, the Arkham Knight and his army took over the now empty mall, and started using it as their hideout, hidden from the public.

Batman: Arkham Knight Incident
Throughout the night, The Arkham Knight broadcasted to Batman from the a bar located on the complex. Later that night, Batman followed a decrypted broadcast by James Gordon, and found the hideout and broke in using the REC. After finding his way to a tunnel used by the construction workers, Batman was ambushed by the Arkham Knight, using a massive excavation drill. Batman tricked the Knight to drive directly into several explosives, as the Batmobile was small enough to avoid them, unlike the large drill his opponent was using.

However, despite this, the Arkham Knight managed to trap Batman to a dead end, and even though Batman managed to escape unharmed, the Batmobile did not, and it was grinded to pieces by the drill. As Batman traveled forward, he entered the mall, and found Gordon tied to a chair, guarded by several henchmen. Batman took down the guards and attempted to free Gordon, but was stopped by the Knight.

Fed up of Bruce not recognizing him, the Arkham Knight finally unmasked himself, revealing that he was in fact Jason Todd, the second Robin, who had seemingly died years prior on the hands of the Joker. This revelation surprised Bruce, who corrected that he hadn't abandoned Jason, as he thought he had died. Jason claimed Bruce was lying, and pointed one of his guns at him. However, Bruce headbutted Jason, which gave him some time to hide. Jason ditched the Knight's visor, revealing a red mask underneath. After combining his pistols into a rifle, he grappled up, and started searching for Bruce from a vantage point.

After the battle, consisting of 4 vantage points and several enemies, Bruce finally managed to overpower Jason. They fell from the vantage point, and just before Bruce started beating him, he pulled his punch. Jason, mask broken, still angry and mentally hurt, told Bruce about his torture, while pointing his gun at him. As Bruce offered to help, Jason put down his gun. Bruce turned around to inform Alfred about Jason's survival, but as he turned back, Jason had already left.

Batman returned to Gordon, and freed him. They started heading towards the exit, an elevator that led to the roof of a newer skyscraper. However, they were assaulted by thugs who arrived with the elevator. Batman easily knocked them out, and waited for Gordon to enter the elevator. As the two headed up, they discussed about the recent events, and the night Gordon first met Bruce.

Riddler's Revenge
Throughout the night, several militia soldiers inserted Riddles throughout the mall. Batman solved them all, and destroyed 15 spider drones.

Trivia

 * If the player solves enough riddles everywhere else, Riddler might mention how the Militia hideout on Founders island is filled with riddles. This can happen even before the player (or Batman) learns of the mall, but this has no effect on the storyline.