Load up New Alexandria on Easy difficulty from mission start. Play through the level until you have a waypoint to Club Errera. At this point, you want to fly back to the hospital and at altitude 360.1, on a platform on the largest tower (near two trees) land your falcon and hit the green switch in the small room.
Get back in your falcon and fly your way back to Club Ererra. Once inside, you will see the Brutes and Grunts having a rave, lead by a DJ brute nearest to the entrance. Go over and stand next to the DJ Brute to unlock the achievement.
If you then go to the top of the building you are on (fly to the top), there is another hidden switch underneath the air conditioning ducts that will change the song. Hit this to change the song to Siege of Madrigal, which should unlock:
For those who prefer a video guide: