once you make your way to the top of the mountain, when soap says to take one of the guards in the the two pairs you encounter, you can either shoot or just let Soap take out all 4 guards. it doesnt matter at this point if you fire, the no alert/injure part of this only applies when the blizzard starts. once Soap goes into overwatch, pay attention to the heartbeat monitor and aim your self away from bad guys. Soap will snipe a few that come in your way but its best to let them walk your path before you go ahead. (i crawled whenever i found a heartbeat too close and i got the achievemet).
IMPORTANT if Soap ever tells you that youve alerted a guard, quickly pause and reload to last checkpoint as there are several auto-saves on this level and you dont want to walk into one right after alerting a guard.
This achievement will pop for you once you have set the C4.