This solution pertains to those of you who have already beaten the game on a lower difficulty. In my case it was beaten on Normal, in full, before attempting this. It is unknown to me if this trick will work on a completely fresh run or under any other circumstances.
I used the Acrophobia skull (allows you to fly around quickly), along with other skulls such as Bandana (infinite ammo), Boom (increased explosion radius), and Cowbell (increased explosion acceleration).
The main skull you need to use here is Acrophobia as it allows you to fly through areas quickly, avoiding enemies and skipping through to further checkpoints.
- Flying higher and faster can be achieved by spamming your jump button and holding down, much like in forge mode.
- Be careful! You can go too fast and splatter yourself upon hitting objects, resulting in death.
- Don't fly too far out-of-bounds or you will die. Stay within the linear path of the mission itself to be safe.
- Take out as many sniper jackals as possible before trying to fly through areas or you will very likely die in one shot, specifically on Sierra 117 and Tsavo Highway.
- Some sections are un-skippable and you must wait for checkpoints to register or kill all enemies to advance, specifically on The Ark waiting for the tanks to be delivered.
- Land often and walk to register checkpoints as often times the game will not give you a checkpoint if you simply fly the entire way.
- On The Covenant mission, wait until you are in the Hornets, flying them, and reach a checkpoint before jumping out and flying to the next area, skipping air combat.
- The Covenant mission again, specifically after the Arbiter kills the Prophet and you're trying to escape the flood, seems to be finicky and you must take your time here killing mostly all enemies without flying too much, otherwise after dropping down the hole at the end the game will not advance and you will have to restart the entire level.
- You will get a warning before starting a mission that achievements will not track, this is true for par-time and par-score achievements, as those will not count here.
- If you're using infinite ammo, my favorite weapons to quickly clear enemies were: brute shot, snipers, rockets, laser, and fuel rod gun.
- Boom and Cowbell skulls work great for launching enemies off ledges and clearing hordes of enemies, like the flood.