From Halopedia, the Halo wiki
The Elevator Courtyard
As soon as the door to the first combat zone opens, toss a grenade to your left to take out the first batch of Crawlers that assembles near the door. Take out any left with the pistol, then swap it for a Boltshot from the dead Crawlers.
The elevator courtyard is divided into two high emplacements, a road in between, and a wide area by the exit where most of the Prometheans are. The left structure is a tall cliff leading to a sniper balcony and landing hangar, the right structure is a small garage with three stories and turrets. To defeat all the Prometheans in this area, one should start from the left to the right.
After defeating the first few Crawlers, head down the hill and look to your left to see a Soldier and two Crawlers attacking a settler. While they're distracted, take them out with your battle rifle and collect any Boltshot ammo that's dropped. Then head up the stairs to the hangar on the left cliff. Up there, there will be a few Crawlers and Soldiers behind a landed ship. Most of them are armed with Suppressors. Due to the ship as cover, this fight can be fought as fairly mid-range, but the Soldiers like to throw grenades. Fall back below or behind nearby stairs if their fire gets overwhelming, and concentrate on headshotting Crawlers and weakening Soldiers with the Boltshot before a headshot. A second wave will come after the first is wiped out. Toss grenades under the ship as they arrive, and defeat them the same as the first.
To the Bridge
The Garage Assault
Tank at the Gate