This question has been asked many times, despite the game very clearly giving the answer, but you MUST use Free Aim for this achievement. Trying to activate aim assist on Hard or higher difficulty will give you the message that turning aim assist on will prevent the difficulty achievement from unlocking.
This is actually good to be honest: Free Aim, once you're used to it, is much more responsive than any aim assist. I've found myself doing less headshots now using aim assist on NYM mode than I did using Free Aim on Hard.
Now, a few tips:
-Don't be so quick to get up after a slo-mo dive. If there is an enemy or 2 left after your dive. Often times, you'll find yourself in good cover and can quickly activate Bullet-Time if you get in a jam. If you try to get up before you know exactly where they are, you'll find yourself scarfing down precious painkillers.
-Dive, Dive, Dive. Yes, cover is necessary in some parts, but most every encounter can be handled by repeated dives. The game will always give you a slo-mo Bullet-Dive, even when your BT gauge is empty. Abuse this, just remember the first tip about making sure you know where enemies are before you get up.
- I would literally dive at most every enemy, even if there was only one. This prevents you from taking damage you would take in a normal gunfight. Just remember, you can use RS to cancel a dive to conserve BT.
-After EVERY gunfight, loot for ammo. Yes, ammo seems plentiful now and you may not be worried about it, but the game seems to randomly get real stingy with ammo really quick at times. I was not always careful, and I ended up spending an hour in Panama at a really bad checkpoint that could have easily been avoided.
-So, weapon choice was really simple for me. I liked carrying one semi-auto pistol (this is single shot, NOT revolvers), one fully auto side-arm. I never dual-wielded, as it seemed to burn through ammo too quickly. One direct hit to the head from a pistol has the same effect as one direct hit to the head with a pistol with 27 bullet holes in the wall behind your target does. Never use the revolver, as the reloading will get you killed.
- "Big" weapon: Anything really. My preference was the reticle though, so remember you can hit "Back" to remove a laser sight or scope. I also preferred single-shot weapons as they were easier for me to get headshots and conserve ammo. I will say shotguns would get dropped for rifles, and NEVER use a Grenade Launcher. Last Stand with a Grenade Launcher....terrible.
-One last thing that the game never makes clear....there are parts in the game where you will be attacked by a soldier with full body armor and a kevlar face cover....oh, and he's wielding a fully-auto machine gun that will make quick work of Max. The trick to this is to NOT dive at this one. Get cover, wait for him to reload, activate BT (RS), aim for his head and keep shooting. Eventually, his helmet will pop off and you'll kill him. Be warned, if you last stand against him and don't get a headshot you better have a second painkiller because if not, you're done.
That's all I can think of off the top of my head. The other solution has great tips too; the important info is you HAVE to use Free Aim. NO AIM ASSIST!!!!!!