Once you get through the ticker-ridden Tunnel, take the rooftop path (RT) and then clear the first level of grubs and then head up the ladder. Make sure to take out the single guy up here as quickly as possible if you're on 'Hardcore' or 'Insane' and then shoot a hole in the hotel roof for Dom using the dead grub's Mortar Launcher.
Jack will then open the door, you'll have to kill a few more enemies. What you will now want to do is grab a mortar launcher before the Brumak comes out of the tunnel, go to the farthest along the balcony you can, as close to the tunnel entrance. Take aim and 'tap' the fire button for a close shot which you need to time right for the Brumak coming out of the tunnel. Repeat this and time your active reloads perfectly and after 3-4 shots the Brumak will be down.
Achievement will unlock before or after cutscene. It differs sometimes.