If at all possible, do the quest at the same time as someone else. Group with them, and you take 3 beds, and they take the other 3. It makes the quest MUCH easier.
Good day, doctor. You will be tested on your ability to triage patients accordingly this afternoon. Should you pass your examination, you will join the prestigious ranks of Horde Trauma.
Now pay attention! The critically injured must be tended to first. After the criticals come the badly injured. The injured should be tended to last. You must save 15 patients to pass this exam. You will fail should 6 of your patients die in triage.