Instructions
Locate the Brute Chieftain. You should be able to see him giving orders to the other Brutes in the room.
Slap a plasma grenade on the Brute Chieftain's back. This will remove him from play, knocking out the most powerful bad guy in the room first.
Focus your fire on the Brute Captain next. He will be wielding a gravity hammer, so you will need to keep him at a distance. Stick him with grenades and shoot him while he chases you around -- he will go down eventually.
Drop your secondary weapon and pick up the gravity hammer. This powerful item will be an asset in the battles to come.
Fight through the drones you encounter along the path to the barracks. They should prove to be more of a nuisance than a threat, easily dispatched with your battle rifle.
Take out the Brute choking the marine in the barracks first. You can do this with a few well-placed shots from the battle rifle. If you save this marine, he will pick up a gun and help you with the rest of the fight.
Clear out the Brutes in the barracks. Use the battle rifle for long-range assaults, and then swap to the gravity hammer when the Brutes close in. Once you clear out the Brutes, you should be ready to proceed to the next objective.