You'll get this quest after you've completed "A New Threat" and "Headhunting".
Ada wants to speak with you. After your conversation install the M-SAT into any robot. That robot needs to accompany you, because the mod lets them open locked doors. So I'd recommend installing it to Ada, but don't give her Sentry Legs; you're going to have a hard time inside the Mechanist's Lair with her restricted mobility. Before heading off, take a few Rad-Away with you, since there are Tankbots, that might explode with 200+ RADS.
Go to the RobCo Sales & Service Center, where the Mechanist's Lair is located, near the Boston Airport. Fight your way through the robots inside the lair until you confront The Mechanist. (If you confront him as the Silver Shroud, you'll get a completely different dialogue).
You'll get the chance to kill or spare The Mechanist and you get to shut down the Facility. Do so and talk to the Mechanist and Ada afterwards and the quest is completed and you get your achievement.