On this page of our guide to Batman: Arkham Knight you will find locations of all breakable objects that can be found in Arkham Knight HQ. Destructible objects are one of secrets (collectibles) available in the game.
In the Arkham Knight's HQ, there are fifteen Spider Drones that you need to find and destroy. Destroying them all means completing three new Riddler puzzles (the counter updates every five objects).
It may be difficult to find the drones, because only some of them are on the floor. Usually, they cling to walls and ceilings so, explore the specified areas thoroughly and zoom whenever necessary (you do not need the detective mode here). After you find a drone, you need to use the electric charge to blow it up.