In order to achieve this par time, nothing more is required other than playing on Easy.
I was able to finish in 4:38 on Easy, so you have plenty of wiggle room.
Just make sure you don't have any x0.00 skulls on.
The only 'trick' in the level is after you ride the elevator, I think the flood has to spawn before you can get the door open. (I tried skipping over everyone the first time and it didn't open.)
Just kill the Covenant in the room and the door should open.
If you need more help than this, I made a video of me rushing through, but it's being crap and not uploading it so I can try uploading sometime if you need it, or you can look at it on the Xbox One.
This video starts as I enter the first door (just up the hill from where you start, on your right.)