You must have the "Hammer of Infinite Fate" DLC for this achievement. The "Disgorger" can be purchased as a Secondary Weapon for the Deuce in the Motorforge for free. After equipping it, simply kill Tainted Coil units outside of General Lionwhyte's castle with the Disgorger until the achievement unlocks. Location of units may differ if the game has not yet been completed.
Posted by Runch Optimus: "Just a note: Kills must be made during open world sections. Any kills during side missions or stage battles don't count towards the achievement."