The par score for Covenant is possible to obtain on normal difficulty with a high enough time multiplier because of the sheer number of enemies and vehicles. The par time for this level is 20 minutes. You will get around a base score of 16,000 before applying the time multiplier if you kill most enemies and destroy most vehicles. The multiplier will steadily decrease after 20 minutes until it levels at 1.00x at 40 minutes.
If you don't feel like relying on the time multiplier, you can put on a few easy skulls instead and take your time with the level. I would recommend skulls like Famine, Fog, Tough Luck, and Iron (Just save and quit if you die, then resume checkpoint to continue with points intact). You probably won't even have to apply all 4, but you might as well to be on the safe side. This is the guaranteed method. You are not rushed and end up with more score than you need.
To track your score and time, you can put the scoring and hud settings to competitive score. Keep in mind that after 20 minutes, your score will start to drop, but you should have more than enough points to stay above 25k.
Getting kills without dying builds up your killstreak and earns you more points. Multikills also give you slightly more points.
This is a big one: DESTROY ALL COVENANT VEHICLES EVEN IF THERE'S NO OCCUPANT(S)! It's basically free points! If a marine on the warthog turret takes out a grunt but doesn't destroy the ghost, hop out and toss a grenade at it until it blows.
At least on normal difficulty, there is another spartan laser by the downed pelican at the beginning, so feel free to use up the one you spawn with and keep the new one for the next part of the level.
If you're driving a vehicle and the turret marine or passenger gets a kill, it gives you points. On foot, their kills won't and sometimes they may even steal your kills.
Destroying the phantom during the hornet part will give you loads of points. Take out the wraith and brutes on the island as well.
Before getting in the tank, I hopped in the gauss warthog and drove it off a cliff so marines couldn't steal kills. Probably not necessary. But if they are taking kills, "accidentally" firing a shell near them an knocking them off a cliff won't take away points.
Destroy the banshees, ghosts, and prowlers during the scarab fight.
Don't kill any flood when they're helping you out during the later part of the level. It'll take away points. You can accidentally shoot the infection forms without penalty, though.
You can always let infection forms reanimate corpses for more enemies to kill and thus more points.
I was able to get 31,000 base score with the 4 skulls. This was also within 40 minutes, so there was a small time multiplier that boosted me to 40k. There's plenty of room for error with this method.
BE SURE TO WATCH THE END CUTSCENE, just in case.
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.