As per the original achievement on X360. The same solution applies, simply follow this guide and video and the achievement is yours!
To recap what you need to kill without getting detected at the mouth of the small area are:
3 Grunts walking around or in a gunner seat
4 Grunts sleeping*IMPORTANT NOTE* Thanks for Darnscenekids and BaronVoNewman for confirming, you do need to be in anniversary mode to obtain this achievement!
This is not my video by the way, credit goes to ADRRGamingUK on youtube