At the end of the mission, the friendly A.I. from the previous mission, Felicity, is
To prepare beforehand, redeem a few Golden Keys from the SHiFT kiosk in Concordia, then obtain several purple weapons; you will be needing a corrosive SMG or laser to make this easy.
When the fight begins, chuck a few grenades and use your action skill to give you a buff while you take down her turrets. You'll break her health bar quickly, and she'll commence a nasty AoE effect that you can easily avoid.
For the rest of the fight, you can get Second Winds off the Loaders she spawns, but be sure to get close to them, as they can and might run away. Spam the corrosive weapon along with your action skill until her health depletes and the cutscene plays.
Turn in the mission and achievement unlocked!