Because of the recent changes to par scores, this achievement is now very easy.
As the end of the level seemingly has infinite flood, you could theoretically do this on any difficulty.
Addition from RadZakpak - Not infinite, but they do spawn for quite a while. So it should be enough to at least get you the par score.
I did a Normal Speed Run of the level, trying to keep a carbine and a sword for the whole run. I only had 7500 points when i got to the last room, but I was able to earn 3000 points off killing the flood with my sword before I figured I'd just end the level.
Edit: I tried doing a straight up speed run where I skipped all enemies until the end, and was not able to earn enough points for the par score, so I am changing the guide accordingly.
So my new guide is - literally just kill everything. Put on the Jacked skull as it doesn't affect the level at all.
When the level starts, a sword flood will run at you. Kill him and take it.
There should be plenty of swords and carbines strewn about or on enemies to get you through the level. Even killing every enemy, the level only took me 10 minutes.