Although Pingy's solution would most definitely work, I decided after dying thousands of times on legendary and only ending with about 12,000 in score, I would try my luck on Heroic.
Edit: This guide was written with a par score of 25,000 in mind. I am sure a lower par score would make for a much easier achievement.
Skulls (8 or 9): Anger, Catch, Eye Patch, Famine, Fog, Iron, Recession, That's Just... Wrong, and Thunderstorm. (Iron is optional. I managed almost 17 minutes with 45k score. You can run without a skull or two if need be and still get par.) Recession and Eye Patch didn't hurt at all as the energy sword was pretty much the only weapon I used.
From the beginning, I used the ghost to get to the first scorpion tank that is in the second area. You can either kill the flood running to it or board the tank and melee a few times (I did the latter). Using that tank, I killed nearly every flood and vehicle for the driver points (at the time of the writing of this solution, vehicles don't award points in Halo 2 although I did see an occasional negative that didn't seem to impact anything when I killed ghosts.)
Once I got to the point where you had to get out of the tank, I used only the sword (and grenades occasionally) and killed flood with the sword and the sentinels when needed with grenade sticks. I typically did my best to run past the sentinels using active camouflage if deemed necessary.
Once you get through to a wraith and two ghosts, I jumped down to the left and stole a ghost. This part comes right after you are exiting the area you had to walk since we were using the tank instead of a ghost (and killing all the flood inside with the sword). There are several boxes in the path with a few sentinels around. The flood was just getting in the ghost as I dropped down, so I was able to sword him out of the ghost. Using that ghost, I boosted to the gondola portion.
I am thinking I had around 20,000 points when I got to the portion where you are on the floating gondola and killed flood there pretty easily on Heroic as opposed to Legendary. I ended with about 45k score after 16:51.
All in all, I believe both Pingy's solution and my solution are viable options.