Like others, this was a tougher par score—personally, the hardest in the game, since for the others I could just blitz through things on Normal with a handful of skulls and be fine. Basically, if you die more than once you probably won't have the chance to get par score because you'll reset your killing streak and you'll lose precious time; if you aren't finishing this mission under par time or a minute or two after, you probably won't get it. You better be used to landing headshots, because that's the only way to speed things up (and get useful medal point multipliers) to make this achievement happen easily.
I ended up setting the difficulty to heroic, with Famine and Fog on. If you want some more cushion points-wise, you can set Iron, but that will depend on how confident you are. Like I said, death is a pretty tough obstacle to this mission, so if you die, especially early in the mission, I think you're better off restarting anyhow. So go ahead, turn on Iron. Do you feel lucky?
At the beginning, clear out the enemies and rush the Scorpion. Use it to smash everything up to the tyrant guns. Once you've cleared the cluster of jackals and the pair of Banshees that swoop down on you, make your way to each AA gun, only pausing to kill Grunts that are immediately in your way; forget about the Elites on the upper levels. Grab a plasma pistol while you're here. Once each is destroyed, beeline back to your Scorpion and hoof it along, blowing up any air enemies when you don't have a ground target to hit. The key for the next area is to be efficient; wasted shots slow you down and open you up to easy deaths. In the next area, kill the fuel rod grunts on the platform, then the Ghosts. In the area outside the Sword base gate, you have two fuel rod turrets, two plasma turrets, and two Revenants to snipe; if you move fast the Falcons will likely still be alive drawing fire and making it easy to spot the turrets. Once these obstacles are dead, run to the entrance to sword base. Kill any Banshees in the air on the way; these will give you some nice cushion points. Since you have a plasma pistol, you can noob combo the Elites in your way, headshot the Grunts on the turrets, and proceed to the service corridor.
In the service area, your goal is to prepare for the final stand defending Halsey's lab, and the easiest way to speed it up is to have lots of needler and needle rifle ammo. As such, loot both from the Jackals as you make your way up the stairwell. When you reach the multiplayer map portion of Sword Base with the stealth Elites, switch to a plasma pistol or repeater and DMR from the nearby crate to conserve your needle rifle ammo while you kill these guys, then retrieve those weapons and push through once the enemies are thinned.
On separate run-throughs, I had between 60 and 70K points going into this final section, which meant I had some cushion in case I ran out of par time. My strategy for here was to arm the A, B, and C turrets only; you want the enemies from at least one direction (D) to come towards you faster to clear waves. A riskier strategy that I employed for more points was to rush towards the Phantom across the bridge over by A and B; you can get a sweet multikill headshotting the Grunts here, as well as scooping up more needler ammo. I then waited over here for the next Phantom to drop at this position, taking cover nearby; when the next wave of Brute and Grunt reinforcements arrived, I just grenaded them as soon as they dropped, headshotted any stragglers, and used the rest of the plasma grenades dropped here to tag and destroy the Wraith still loaded in to the Phantom, and then hoof it back to Halsey's lab entrance while avoiding the stray dropship concussion round. I got a ton of points and took out the Wraith that would potentially run my day with an unlucky mortar.
With your needle rifle and needler, you now can decimate the Brute waves as they arrive, then pick off any Jackals behind them. After the Brutes you'll get a bunch of Elites, so I switched to plasma pistols I looted from in front during combat lulls and the DMR (so the Elites didn't jump around and waste my ammo.) Here your goal is simple—headshot grunts, two shot Jackals (hit their shield notch + headshot when they stagger) and noob combo Elites that are close. On Heroic, you can whittle down their shields with DMRs easily as well if they're too far away for the plasma pistol to track. When new waves are being dropped, take the opportunity to use the Spartan Laser (right in front of the lab door) to kill Banshees for easy points. You'll know you're at the very end when a Phantom parks itself right in front of you and drops a bunch of Elites and FRG Grunts. Kill the Grunts first, and if you still have laser ammo you can use it on the gold Elite. You only have to kill a certain percentage of the wave to get a final checkpoint and Halsey will tell you to come in; run over to the door controls and you're done.
My final score on my first successful run was 69,461 and 22:02. Hope these tips help you.