Progress through the story in the AWE DLC. The mission called "A Dark Place".
You'll arrive to a huge room (Active Investigations) with an elevator in it. There is darkness around, which drains your power.
Enter the elevator and press the button to summon Dr. Hartman. Don't fight him, just concentrate on getting power cores in their place. Stay in the light to avoid damage. The first core is right in front of you, pick it up and shoot it at the socket on the northeastern corner. The light will turn on and you'll see more cores hidden behind wall panels. Tear them out and place them in their sockets as well. One is east from the elevator, one is up on the southern balconies and one is at the highest point near the western wall. Next to this one there is a switch too, press it to turn on the light and finish the fight.
Take the elevator up and activate the intercom to unlock the achivement.