Batman: Arkham Knight on Xbox 360? No—Only PS4, Xbox One, PC

No. Batman: Arkham Knight (2015) released only on:

• PlayStation 4
• Xbox One
• PC (Steam/Epic — initially broken, later fixed)

The Xbox 360 / PS3 hardware cannot run the game's engine, open-world streaming, or Batmobile mechanics.

On Xbox 360, play Arkham Asylum, Arkham City, and Arkham Origins — all excellent.