This achievement is almost impossible to not unlock during the DLC story arc, but there is still the possibility you do not have it.
You will have to destroy 4 drone types
Extractor drones: Needed to be destroyed in the first misson.
Suppression drones or Tank drones: You are told to destroy one in the first mission aswell.
Light drones: These fly around everywhere and should be easy to find.
Large Drone: Less common than light drones, but still should be no problem finding them around.