This trophy can be unlocked on any difficulty, the key is not dying or reloading your checkpoint. Because the game has two trophies with required difficulty, you can either get this on these runs (Suicide & FUBAR), or come back and mop this up at the end and play on easy (Walk on the Beach).
This is easiest to obtain during the first chapter, Chapter 1: The Evacuation. When you start the chapter, switch to your pistol and use only this weapon. This will allow you to control your rate of fire, and how many shots you take.
When in a confrontation, use the Battle Management system and have your squad do most of the fighting by pressing R2 and directing which member of the opposition to to kill. When firing, aim for headshots, and do not fire unless you are comfortable the shot will land. These do not all have to be kill shots, they just need to hit their intended target - so no blindfiring.
In the first chapter, after a bit, you will be told to switch to silencers. Do this, and take out the guys closest to you to get your hit counts up. Use your squad for the rest of the mission, and when you get to the end of the chapter, there will be a slow motion part, which will guarantee you several hits. You can essentially have your squad do all the fighting, and only shoot during this slow motion portion, and as long as you do not die, you will unlock the trophy.