Notes for par scores on all levels:
Par scores are heavily influenced by par time.
Note: Competitive Score shows the time multiplier bonus; Regular Score does not. The time multiplier bonus still exists in Regular Score, it only shows up at the end of the mission. With Regular Score, you may not see the time bonus, especially on longer missions (credit: EaseAndInspire)
During "par time" all scoring is tripled.
After "par time", you have 10 minutes where your multiplier goes from 3.00x down to 1.00x. For example, if you kill an elite for a pop up of "+200", the score will show 600 during par time, but then will trickle back down to 200 when the multiplier goes down to 1.00x (and will be 400 if the multiplier is at 2.00x).
After the "ten minute down to 1.00x" period, one of two things happen:
1. You get a 2nd grace period, of about 10 more minutes. Multiplier is already at 1.00x so nothing else happens with it.
2. All positive scoring is done. All kills show up as red "0", but you will still lose points for dying, team kills, or checkpoint resets.
After that (Par time + 10-minutes + possible grace period), all positive scoring is done no matter what. Negative scoring is still active.
If you've already achieved the par score, you'll still have to beat the level while making sure you don't have enough negative scoring (deaths) to go below it.
For this specific mission:
Level: Pillar of Autumn
Par Time: 20:00 minutes
Par Score: 25,000
Skulls: Catch, Famine, Fog, Thunderstorm, Tilt, and Cowbell (non-scoring but accelerates explosions)
To get the par score, you'll need to save time by running through some of the easier (lower scoring) areas. At the beginning of the mission, stay to the right and keep sprinting to the Mongoose. The building right before the Mongoose has a DMR and Rocket Launcher. Pick them up and drive the Mongoose straight through until you reach the tank area. You should get there in under 3 minutes.
Use Rocket Launcher to destroy tank (Vehicle kills are worth 800-1000 points, and you can't take the tank anywhere). Once the tank is destroyed, you can run to the next area (the cave) or kill the brutes for about 200 points each. You cannot run though the cave due to the flying enemies, so you will have to kill them (also helps that the flying enemies are worth 200 points).
Before you leave the cave take the Spartan Laser if you have less than 5 rockets left. This will be needed to take out the Hunters later. After the cave is a big area with a lot of enemies, followed by a small transition point with stairs (that has a sniper rifle and another Spartan Laser) and then a 2nd large area with turrets and Ghosts.
You can pick off smaller enemies in the first large area, sprint through to the stairs, and then take out the turrets in the 2nd area. With the turrets out in the 2nd area, you can climb the upper / roof area and then drop down into the building. There are 2 silver elites and some grunts you'll have to kill.
You'll have to fight in the next few areas, including a section going up. Search around and you'll find more DMR ammo to take out both the snipers and shielded enemies. At the bottom is an elite with a sword. At the top is another silver elite.
Then you're at the hunters. Use your spartan laser or rockets (plus grenades) to take them out quickly. After that, you are in the last area.
In the final stand area, there are a lot of enemies in a short amount of time, and the bonus time (post par time and post multiplier countdown time) is actually 15 minutes giving you a total of 45 minutes to score points for the full level. This area is the best to make up points. I got 6000+ points within the 15 minutes.
For the final part of the mission, you use the MAC Cannon. If you've been able to run through the whole mission, but are still short on points, the MAC Cannon will easily make it up (as long as you are under 45 minutes). You can even kill a few vehicles that you need, and then exit the Cannon and wait for the final firing signal to end the level (after that hop back into the Cannon, fire the shot at the red part of the large ship. Right after you fire the mission will end).
For me, I got into the final room at about 23,000 points. Luckily, I killed all the elites and ended with 25,083 points, but was out of time for the MAC Cannon. Good luck!