First thing you need to do is complete the Prologue at least once so you know where the enemies are and when you need to be careful.
Now, at the mid-mission screen it gives you 3 choices. Resume, something else, and exit game. Exit game. Now load up the Prologue again but make sure you are on Cadet difficulty. You need to do this entire tutorial/mission without getting shot. If you take 1 bullet, you fail the trophy requirements. You can always reload checkpoint if needed.
I don't have any tips that will ensure you get this other than you need to shoot true. When you scope up, you must kill whoever you are aiming at with 1 shot. If you miss, duck down. It make take you a few times to get it but this is by far the easiest mission to do without taking a bullet. So have some patience and you will earn yourself a very nice trophy!