Edit: Took out the Legendary guide since being able to do it on Normal makes it irrelevant.
Notes for Normal
This is easily achieved on Normal so this is just my guide for streamlining the level as much as I can. This isn't a handhold level guide, it just streamlines the level so you don't have to waste as much time.
I used no skulls.
I'd recommend having one precision weapon and one power weapon at any time. All medals give bonus points so headshots are a consistent score boost you can get.
When the level starts, stick to the right of the room to grab extra Pistol and Assault Rifle ammo. Grab the Sticky Detonator from the dying cop if you want but I'd recommend keeping the Pistol. From here, just kill your way to the airlock area.
There's a DMR in the room with the scientists if you want to replace the Pistol. Just close the doors as soon as you can as you don't need all of the kills. Even if you rush the door one Phantom with Sword Elites should make it in, but that's it. After this you just kill your way to the Hunters. Either grab the Shotgun right outside if you're feeling frisky enough to shoot them in the back, or grab one of the many Sticky Detonators in the room to kill them.
After the cutscene, proceed as normal until the first room with the small airlocks. You can actually skip this room by just going to the door at the other end. You do have to fight at the second one, however. I just pushed the buttons on the doors as the enemies came in to send them back out the airlock.
Once you get to the Mantis, just focus on killing at least one Phantom per pair. I had one pair where I killed both but that was it.
I had a time of 15:59 (par is 20:00) and got a score of 41964 (par is 25000).
I had 0 deaths, so I probably got a bit of a boost from the killstreak, but as you can see, even by skipping many enemies (all 3 airlock rooms at least) I was able to get the par score by a wide margin.
The Phantom kills and the Time Bonus are going to be the majority of your points, so just be careful as you go through the level. Its better to take your time at parts to stop yourself from dying than to end up dying and losing your streak AND having to go through a part again.