Haloruns record page: http://haloruns.com/records?lb=0805 (click the timestamps for video links)
Watch Video: Halo Speedrunning Tutorial - Part 6: Evacuation
As soon as you gain movement control, turn slightly to the left, run, jump and thrust off the platform. This skips the spawn for all the enemies in the driving section. Once you reach the crashed pelican, get out and Its just a matter of clearing everything. The splinter turret is useful for clearing groups of crawlers. There are several enemy spawns that get triggered as you progress closer to the door. There are two soldiers that spawn up by the gauss turret that will either spawn by walking up the stairs leading to them, or after killing one of the two soldiers to the left upon first entering the area.
Once the door starts opening get through as fast as possible and run forward until you hear sloans dialogue. Then run back outside and grab the turret outside the door and break it off. After a few seconds you should be teleported back inside. Use the turret to kill everything and push the button. Each of the 3 waves on the elevator is on a timer based on when you cleared the last one. Grab the railgun and any splinter grenades you can find and line up to kill the first wave. This can effectively be done by using 2 splinter grenades. Now you can line up for wave 2 which consists of several soldiers. Once this wave is cleared you can line up for wave 3 which is just 3 knights. The white incineration cannon knight always spawns in the same place so line up to kill him first using a splinter grenade and finish him off with a railgun or scattershot if necessary. Grab his incineration cannon to kill the other 2 knights which spawn in random locations. Now just line up and get ready to exit the elevator. Locations for all 3 waves:
run through the hallway and start clambering your way up the structure. Once you reach the top, its just a matter of getting to the pelican to end the mission. The animation where you get knocked down can be skipped by being as far left as possible against the wall.