There are a total of 15 Destructible Objects located in the Arkham Knight HQ and they can be found in the following locations:

Breakable Object 01

Just before attaching the Power Winch to the anchor point and driving the Batmobile over the edge into the fan shaft, look on the wall to the right to find this Spider Drone.

Breakable Object 02

This breakable object is on the left hand side of the fan shaft, close to where we entered from.

Breakable Object 03

Attach the Power Winch to the anchor point and drive the Batmobile over the edge into the fan shaft. Look up towards the top of the room to see this Spider Drone on the wall above you.

Breakable Object 04

This breakable object is on the right hand side of the fan shaft, between the two fans.

Breakable Object 05

Glide over to the platform between the two fans and look for the ledge we grapped up by the elevator earlier. There is a Spider Drone on the wall here.

Breakable Object 06

This Spider Drone is on a wall in the passage on the eastern side of the fan shaft room. It is situated just below the second fan.

Breakable Object 07

After reaching the bottom of the first elevator shaft, exit into the next room and look up onto the wall to the right near the far corner. There is a Spider Drone here.

Breakable Object 08

From the bottom of the fan shaft, grapple up to the ledge on the northern side of the room to find this Spider Drone on the left hand wall.

Breakable Object 09

This Spider Drone is located on the bottom of the elevator at the top of the second elevator shaft. This is opposite the Sentry Gun behind the fence in the western passage at the very bottom of the fan shaft.

Breakable Object 10

This Spider Drone can be found in the area where we had the Arkham Knight boss fight. This is in the eastern room on the left hand wall as you enter.

Breakable Object 11

This Spider Drone can be found in the area where we had the Arkham Knight boss fight. This is in the southern room, high up on the left hand wall as you enter.

Breakable Object 12

This Spider Drone can be found in the area where we had the Arkham Knight boss fight. This is in the southern room, on the ceiling of the lower level, below the escalator and the vantage point that the Arkham Knight used.

Breakable Object 13

In the western room of the Arkham Knight boss battle area. This Spider Drone is hanging from the roof in the middle of the lower level.

Breakable Object 14

This Spider Drone can be found in the area where we had the Arkham Knight boss fight. This is in the western room, high up on the left hand wall as you enter.

Riddler Trophy 15

In the northern room of the Arkham Knight boss battle area. This Spider Drone is located on the ceiling inside the Chinese restaurant.