Crysis

For this achievement you will need to kill an enemy soldier that is wearing a nanosuit with a "power punch"

To do this, you will first need to use your fists (not the gun melee attack), hold down Y and press down twice to equip your hands, then run to an enemy wearing a nanosuit, press RT until he's dead, cheevo unlocked

The first time you encounter the nanosuit-wearing enemies is on the mission titled "Relic", after the excavation area when you are proceeding to the landing zone to be evacuated via VTOL. The objective will be to secure the landing zone, and several nano-enemies will arrive. They are easily spotted either by their ability to cloak, or their bright glowing eyes.

*NOTE* I had to kill several nanosuit enemies with a power punch for this achievement to unlock, good luck!

You can do this on Level 6 "Awakening" very quick.

Take your way to the landing zone. There is a Nanosuit soldier going around with a Minigun. Go into cloak mode (RB) and sneak up behind him. Equip your fists (hold Y and press down on the D-pad two times) and punch him a few times - Achievement unlocked!

Note: I deactivated cloak mode when I was near enough to punch him - I don't know if this solution works when you are still in cloak mode.

While the other solutions are good, there are a couple of errors.
First, yes you do need to not be holding a weapon (or grenades). Select the hands by pressing Y and then down on the D-pad. Some solutions are saying right trigger to hit but after 10+ attempts, this did not seem to work. After looking up the control layout (Options, Controller Settings, Player Controls) it shows that for a strength melee, press and hold on the right joystick. First time I tried down on the right stick and got the achievement.

The confusion over a Strength punch might be why people are thinking this is buggy.

Also, the best place to get this is Awakening at the coal mines. I followed the tracks and went behind the buildings. climbed 2 sets of ladders, crossed to the next building on the grain belt and jumped onto the catwalk that has the chain gun. At the bottom of the stairs there is a nanosuit enemy that patrols the front catwalk turning just at the stairs. If you go down the stairs cloaked, you can take him by surprise with one or two Strength punches. Very easy and no shooting required once you get to the building (assuming that you keep in stealth).