HaloRuns record page: http://www.haloruns.com/records?lb=401 (click the timestamps for video links)
From the beginning, go left along the wall, ignoring the enemies. Your goal is to reach the Phantom, which will drop off a Ghost piloted by a Brute. Once you get to the Phantom, wait under it, just behind the Ghost, and hold the Reload button to hijack the Ghost as soon as you are able. Turn around and boost through the level, only stopping by some crates to grab the beam rifle.
Once you pass through the barrier to Kizingo Blvd., head down the street and turn around right before you approach the roundabout. Head back to the yellow truck and if you haven't gotten the plasma pistol, get one from a Grunt or Jackal. When the Banshees approach, aim and charge the Plasma Pistol at the Banshee which will come down. You will need to make sure it is upright and charge it again as you have less than 5 seconds to board it. Take the Beam Rifle and shoot at the toes of the Brute as you are holding the action button. This strategy is only viable on Easy and extremely hard to pull off efficiently on Legendary.
Alternate Banshee Jack
Video tutorial by Aura: http://www.twitch.tv/thatauraguy/c/4235211