At the start of the mission, skip the cutscene. As soon as you see the level load in, jump and hold the movement stick about 45-60 degrees to the left with about 50-75% force. You should land on the staircase below you and slide jump onto the flat platform above the far side of the stairs. From here, jump off of the platform and land on the lower staircase, ideally about halfway down. While doing this jump, time a frag grenade throw so that your slide jump forwards off the staircase coincides with the grenade detonation for an additional forward boost. Jump a few times after slide jumping off the staircase to carry your momentum past the patches of grass.
Meanwhile, a phantom will be dropping off several waves of enemies. If possible, kill grunts that block your way and any others you can kill without losing time. These grunts can drop grenades that can help with boosts later in the level. After making your way past these enemies, head towards the corner where the pale red covenant box is. Throw a frag grenade at this box to prevent it from blocking your direct path, then jump over both the car and box (if applicable) and make your way around the corner.
At the corner where you rendezvous with the marines, hug the left wall. This wall is a great place to bounce your last frag off of to boost yourself forwards. Walk just to the left of the center column, then head towards the corner on the right wall. Upon rounding that corner, you will encounter several brutes. As long as you haven't made any noise (shooting, etc.) after the approximate area of the column, the brutes should not be alerted. Walk towards the next area in the most direct path possible, jumping over the grass patch. Two brutes may block your way. If they are walking and look like they are about to block your way, fire your pistol to alert them and freeze them in place. Once you're on the grass patch, do a slide jump off of the nearby staircase and move to the next area.
The next area has two paths you can take depending on your skill level and knowledge. For beginners and those without a solid understanding of the physics in Halo 3: ODST, the path is much simpler; simply walk to the left of the sandbag and to the left of the truck until you reach the next area, killing whatever grunts you can. However, if you are going for a really fast time, hug the right wall and pick up three frag grenades from the box on the ground in front of the sandbags. Almost as soon as you pick them up, jump over the sandbags. Once you reach about the apex of your jump, throw a frag grenade at the wall of the platform perpendicular to the stairs, about halfway up and as close to the corner as you can get. Continue walking forward, jump on the car, then immediately jump up. If you did it all correctly, you should land on the higher platform with the assistance of the frag. Once you're on the platform, it's time to set up the box launch. Turn around and throw a frag grenade so that it bounces on the ground, bounces off the plasma battery and lands somewhere between the box and the plasma battery. Make sure the grenade doesn't land right next to the box or it will most likely kill you. While the grenade is bouncing into position, press yourself against the box so that it is between you and the grenade. You will want to stand on the left side of the box (if you are looking at it head-on) right on the creased area. Once the frag and plasma battery explode, jump immediately to get launched into the next area. This trick is very high risk with very low reward, saving only about 2-3 seconds optimally.
Again, the next area has two paths you can take depending on your skill level and knowledge. If you are just starting out, the best path to take is a B-line directly to the door. However, a fast time requires a truck launch. To do the truck launch, you'll need a plasma grenade. There are multiple setups for the truck launch, but most of them follow the same similar formula. Start by walking to the left of the truck on the sidewalk section. Throw the plasma grenade down directly to the left of the big green box so that the grenade lands right on the small slope between the sidewalk and the street. Quickly run under (MCC) or over and around (OG) the truck and stand crouched where the box is going to land. A good way to line yourself up is to stand about a foot behind where the two tiles of the street make a corner. If everything went correctly, the box with land on you and launch you towards the door. Be sure to jump a few times to carry momentum. A super fast launch can save up to 8-9 seconds, but this is very inconsistent and requires a lot of precision. After getting to the door, open it with the action button and proceed to the next area.
After going through to doorway, jump and use the slope of the barrier in the road to get a slide jump, then continue doing slide jumps down the hill, being sure to jump over the exploded wraith. Once over the wraith, hug the right wall and kill or jump over any enemies in your way. At the corner, hook a right and walk toward the left side of the truck, then towards the door that the hunters open. This is a good area to do a grenade boost or two.
Once you make it through the door, you will be in the final area. Hunters can occasionally hit you in the back and propel you forwards, but the odds are low. Hug the right wall again, and jump onto the grassy patch. Jump off of this path and attempt a sliding edge boost off of the staircase railing, possibly aided with a frag grenade. A good trick to increase your odds of landing in the right spot is to line up your pistol reticle with the edge of the railing so that the railing edge splits the reticle in half. Once you get the slide, jump to carry momentum and make your way towards Dare's pod. Open the pod by holding the action button to complete the mission.