
There are a couple of ways of skipping the door closing on you. Once you reach the main building, drive your warthog in and proceed towards the door.

This will help you to survive until the door skip easier. You should pick up the overshield by the crates before you get in the Warthog. Grenade is swag strats but also a bit faster, go for it regardless no negative effect.

Use a grenade to tip it upright and hop in, continuing around the island.

As the level starts off and lets you out of the Pelican, immediately head left away from combat and run around the island.
