As with all other par times - do this on Easy.
When the level starts kill all the enemies and the AA tank. I thought skipping them would be faster at first but then the ghosts in the next area didn't spawn. Grab the Fuel Rod from the Brute Chieftain. I'd suggest keeping the Spartan Laser as well.
Wait for the Pelican and take the Mongoose. Drive it all the way up the hill and ramp off the cliff when you get to the open area. Drive towards the entrance but watch out for the Prowlers that come out. Stick to the wall on the right to dodge them. Fuel rod everyone in the hallway then make a beeline through the structure to the elevator. If you kept the laser it should 1-shot the chieftain. Kill everyone then hit the button.
Head back down the elevator and rush back outside. Take the mongoose that's parked near the wall outside (unless yours is in a convenient location). Rush back to the beach.
With the Hornet, rush straight forward and around the cliff. I killed the AA Wraith on the way but not sure if it's necessary. Kill the enemy phantom and the enemy Wraiths then head inside. Feel free to kill whatever brutes you want while in the Hornet. I killed all of them and still made par time.
Once inside, same thing as before. Rush through, elevator, kill enemies, button.
Rush back outside and grab the Warthog. The mongoose isn't much faster and the firepower can be helpful. From here drive straight to the next Hornets.
Shoot each Scarab in the leg, then shoot the back of it off. You can then hit the power core to blow them up. Once they're destroyed head to the top of the ramp before the big building.
When the Arbiter and the Monitor land, I think you have to get out of your Hornet to trigger the bridge, but then just get back in and fly across. After the cutscene just start rushing forward. The only time you actually have to fight is at the second doorway. It will not open until you kill the Chieftain. He has invincibility and will probably activate it. After you kill him just keep on forward and hit the button at the end.
From here on out it's just a straight run back to the elevator.
The only real factors to this run are how well you can drive and how quickly you can kill the few enemies you have to fight.
I believe I died once and that was at the Chieftain near the end (Gravity Hammer concussion knocked me off).
Downvoters please comment.