This is exactly the same as all the timed training sequences in that other FPS franchise I can't remember the name of right now
Make sure to set your rifle to single shot by pressing
before starting the run. You want headshots since they subtract precious seconds from your total time. You'll probably need a few runs to get it down but with a bit of practice and patience this is very doable. Here is a neat video that shows the ways:
Video credits to
PowerPyx on Youtube.