The par score for Crow's Nest can be obtained on Normal difficulty with several easy skulls activated. The par time for this level is 20 minutes. If you know where you're going, you can hit par time and get a 3.00x multiplier that will boost you past 25,000 score.
You'll want to run through the level with your trusty BR and plasma pistol combo. Use the pistols charged shot to take off brute armor and switch to the BR to pop them in the head.
You should run with the competitive score setting so you can track your time and score as you play.
Getting kills without dying builds up your killstreak and earns you more points. Multikills also give you slightly more points.
Famine - Weapons dropped by AI have half ammo. Be sure to replace your plasma pistol often.
Fog - No motion tracker. Not a very open level, so you won't need this anyway.
Iron - Dying restarts the level. You can always save, quit, and resume to continue with points intact if you do die, but your time will add up. Doing this will also reset your killstreak, meaning you'll get less points per kill until you build it back up again!
Tough Luck - Enemies dodge more, brutes are enraged often. They'll dodge grenades but you'll get easy melee kills on berserk brutes.
You can start heading to your objective right away when the level starts.
Use stationary turrets in the hangar bay to take out the phantoms' turrets asap, then use it to kill the enemies it drops off.
Break the turret off the stand and carry it to the room where a swarm of drones attack. You run a bit faster with a turret if you walk diagonally. You'll massacre the bugs with it.
Anytime you have marines with you, they may rob you of kills and thus points. Be quick about those headshots!
You can kill pretty much everything and still hit par time as long as you're quick and thorough.
I was able to finish under par time with 30,000 and managed to kill almost everything, so you have a bit of room to make mistakes.
Unfortunately, the par score achievements in this game be can stubborn about unlocking. Personally, I had to play through the final level several times for the achievement to unlock. You may want to wait for a patch if you don't feel like testing your luck.