Kill an enemy with a Turret Drone explosion.

For this achievement you need to fully upgrade your drone so that it explodes when it is destroyed. You buy the upgrades from the merchants in the Trade Coalition settlements, there will be 1 available upgrade in each settlement for a total of 5. Once you have done this, you can throw the drone out into a group of enemies and then quickly shoot it yourself to destroy it, causing an explosion and hopefully killing an enemy.

A visual aid, should you need it: