I did Par score AND par time for this achievement by doing this method. Kexol has a great solution but I have a different way of going about it making it easier for you and getting more out of it. My time was 8:06 with a score of 26,587 acquiring Par score and Par time, I could have gotten a higher score but once I hit 25k I didn't go out of my way for it.
Skulls: Fog, Catch, Tough luck
Following Nak3d Eli's video on my solution or Kexol's solution you are going to want to head to the right towards the objective, but do know where the video leads to before doing this so you don't get lost. When near the right objective you are going to want to use the Spartan Laser on your Pelican which is most likely the
button unless you have the controls set up differently. Kill the enemy Phantoms and you will get about 17 or 18k points, after they are all gone just go ahead and skip most of the level using the video. (Destroying the Phantoms was Kexol's idea I believe so credit goes to him for that bit)
Nak3d Eli does it quite well so if you do basically what he does you will hit par score except hes fighting Legendary enemies, you are fighting Heroic enemies, you will feel the difference. When I got to the hunters I used the Railgun, grenades, and the Fuel Rod to kill the hunters, they died very quick, if you ever died just quickly restart from checkpoint.
I did this 2 times, the 1st time I got 35k points easily but doing the Save/quit method with iron skull seems to sometimes glitch the achievement and you have to do this over again, I have had to re-do many Halo 4 levels for par score because they were not unlocking.
Note: If somehow you are not hitting 25k points, there are more enemies to kill in the area with the hunters, just kill a bit of them to 25k and skip the next area, everyone should have 25k as long as you do the phantom part in the beginning.