Load up the mission on Easy with the Pinata skull and as soon as you start, kill all of your teammates. Once the second door opens, cloak and jump past the two Elites on guard. Go down to the back of the elevator and activate it, then go back around and fall onto the platform as it descends. Luckily, you will not take fall damage by doing this.
Once you reach the downstairs area, cloak past the Sentinels and Heretics and activate the blast door, allowing your friendly Phantom to enter. As soon as it opens, run past all enemies and enter the open door. For the rest of the mission, be sure to to spam grenades. If you run out, simply melee an enemy. When you get to the final stage of the mission, rush at the Grunts and Elites and grab the Heretic banshee. Fly straight ahead to the opening, kill all the enemies in the area, and voila!
You should achieve mission completion in less than 4-6 minutes! If you found anything wrong with this solution, please comment before voting down. Happy hunting!