Play any of the Armoured Kill DLC maps. For this achievement you will want to either be defending on Rush, or not have the gunship marked flag in Conquest.
You will need to spawn as the Engineer class, and it is recommended that you use the "SA-18 Igla" OR "//NAME?" to lock on and shoot down the ship, although you must be standing practically underneath it. It may take more than a few shots, so you may need to respawn and shoot at it more.
Another option which might be easier for some is to shoot the ship using a Jet or Chopper, just take your time coming up behind it and put as many bullets as you can into it.