This opportunity takes place near the beginning of the mission. Once your front line gets pushed back, you'll be asked to get on the helicopter machine gun. As you do this, 5 enemy helicopters approach, and you'll want to take them out quickly.
Later on, you'll be told to run to a farm through an open field. As you run through the gate in the field, notice the 3 RPGs, and pick them up with the ammo. Immediately turn around and shoot the 3 helicopters behind you, starting from left to right. This will have you take out all 8 helicopters in the mission to unlock the trophy.
Shooting your first helicopter down with an RPG will also unlock: