This achievement you can obtain on the mission Into the Furnace
and it consist for you to reach the top of the mountain on Barkov's entrance/Warehouse. Very simple, just load up your game on Recruit and USE ONLY
your Missile Strikes clicking on the
I haven't test shooting with the guns you carry, just use the missile's strikes.
Take your time, keep dodging the bullets and take cover behind concrete, tank, trees and so on. I also recommend taking couple of helicopters that drop enemies because it'll be much easier for you to progress. For the Littlebird Helicopter I managed to destroy it with the Missile Strikes as well.
When you enter the Warehouse just go down the stairs a bit and the achievement should pop for you. Any suggestions you might have I'll be glad to add here.
edit: People are reporting that even if you throw a nade and even if it doesn't kill anyone the achievement may not unlock. So make sure not to fire any weapon or throw a grenade, and try to focus only on the drone.
edit2: Thanks to Maka91
for providing us a video showing how to do the achievement for those who are struggling or prefer a video perspective.