Your mission is to bail out the Hacksaw squad and save them from the Covenant attack. However, if you play on anything more difficult than normal, the Covenant will generally be able to slaughter all of them when the going gets tough. They will only serve as useful distractions to draw away enemy fire.
You begin standing in front of three or so ammo crates with plenty of weapons. Grab an Assault rifle and Shotgun, because the first fight is in close quarters. Sprint to the nearest Marine holdout and eliminate the two Grunts and their boss. Two more Elites drop in just outside the little room, deal with them the same way. You'll be firing at nearly point blank range, so it's an easy fight.
After Palmer gives command of Hacksaw squad to you, swap for a Battle rifle and shoot the Grunt on the Shade to your left. The next squad of Marines are in the structure ahead, attacked by an Elite and three or four minions. Deal with them how you like, and a drop pod will deploy some more foes. Blast the two Elites with the shotgun and mop up the rest with a pop to the head with a Magnum or BR. Now swap your shotgun for a Rocket Launcher inside the second structure and move around to the last Marine squad.
Snipe the Jackals and Grunts from afar, then deal with the Elite and Grunts that follow up. Keep you distance and turn to your left when Spartan Miller alerts you to the presence of a Wraith. Wait for the Wraith to drop (or just before, when the Phantom is holding still) and blast the Wraith. You should have enough to kill it before it can react, but if you're a poor shot with the Rocket you can bring a Plasma Pistol to hold the Wraith in place.
The Marines are all together now, and this is the part where they are all hopelessly slaughtered. Two waves of Covenant drop, Two Elites and some Grunts and Jackals. Deal with them, but get ready to find cover in one of the structures, because the next wave is trickier.
A Phantom drops a Covenant Squad on the far side of the battlefield with an Elite carrying a Fuel Rod cannon and a Grunt with the same, escorted by Jackals. Closer to your side, a few Elite drop pods will drop a Zealot with a Sword, and another with a Concussion Rifle. If you aren't careful they can all attack at once. If you have any Rockets left, use them on the Elites (remember to aim at their feet, not the body!) and if you run out run inside the nearest structure where the Marines were pinned in and grab a shotgun. The Elites aren't very good at fighting you this close since they can't actually shot their weapons this close, with the exception of the Sword Zealot. Once their mopped up, head to the far side of the big building where the ramp is. Assuming the Hunters weren't drawn to you earlier (which can sometimes happen) refill your rockets and eliminate them. Do the same with the Ghost, using a Plasma Pistol if you need a little extra help. Deal with the last Elite at the top of the entrance ramp with your weapon of choice, and you're almost done. BEFORE you reach the marker point, restock on rockets and grab a shotgun if you don't already have one.
Once you reach the top, Miller alerts you to Phantoms about to appear. Immediately head down to the lower level (2nd floor) of the big structure and either camp at the top of the staircase or look out over the balcony overlooking the entrance ramp. Four angry Elites drop down, 2 with Swords and 2 with Concussion Rifles. If you can pull this off, a few rockets can get the jump on them and blow them away. If any escape they can be dealt a shotgun blast at the top of the ramp.
Once this is done, nothing stands between you and the Phantoms. Use the either the Spartan laser or Rockets to finish off the Phantoms and you're done. Palmer will, however, give you a reprimand for failing to save the Marines.
(Technically, it wouldn't matter how many Marines you save, since in the next mission the Pelican you boarded is shot down and you're the only survivor!)