You will receive the start if the questline for this as you adventure around the wastelands.
*** Spoiler - click to reveal ***As you head south towards Diamond city you will receive a pop up message on your screen telling you to tune into military frequency AF95, do so to start the questline 'Fire support'
Progress to Cambridge police station & assist in killing the waves of feral ghouls then speak to paladin danse.
The quest will shift to 'Calls to Arms' proceed with this quest & you will reach ArcJet Systems, enter with paladin danse & continue through killing the terminator style enemies clearing out the entire facility.
You will eventually arrive at circular room where you must head out to the back & hack a terminal. Do this then either kill the enemies or close the door to the left of the window & start the engine, when this has finished speak to paladin danse once more & enter the lift.
Follow the path around to one final room killing more terminator style enemies & then exit the facility.
Outside speak to paladin danse again & just to be safe, use any positive choices & he will offer you a place within the brotherhood, accept & then travel to the police station, speak to paladin danse one final time & after the conversation the achievement is yours.
Here's a video showing you from start to finish how to do this, all credit for the video goes to Alex from RandomChievo's.
Warning, video contains spoilers.