This achievement is missable and/or bugged. It didn't unlock for me on my first playthrough, which was on Hard. I replayed the level on Easy and it unlocked straight away. (Edit: Though it doesn't say it in the description, a death during the level will prevent you from getting the achievement. Do it all in one go.)
Chaffin is the solder who gets shot shortly after the first time your squad breaks into two groups. You drag him to safety, clear the street and then move up to the roof. Take out the sniper with the AT rocket, and move to the NW corner of the building as directed. Switch to your secondary weapon which has a high-powered scope and prepare to take out enemies on the street.
After taking out a group on the street, a member of your squad says that there are guys on the rooftops, so take them out. The Marines on the street will move up to the next cover and more enemies will spawn on the street and balconies of the second floor of one of the buildings on the left side of the street. Take them out again, and yet more enemies will spawn on the street (one of the squad members says something to the effect of "Oh fuck" at this point).
After that group, the Marines evac Chaffin to safety (you can zoom in and see them carrying him into an alley). As soon as your squad member asks "Can we get off this fucking roof now?" the achievement should unlock.