The second visit to the surface is very similar to the last one. Start off by attacking the mercenaries by the barricade. Further on, focus on the Xenomorphs which will be trying to get close to you and O'Neal, as well as Spitters; it's best not to let them take any of your health and armor points.
Keep moving forward, pick your targets carefully and pay close attention to what the aliens are doing. Make sure to clear the upper galleries - single mercenaries may be hiding there, and wait for the heavily armored soldier to appear; when he does, focus solely on him.
When the battle ends, search the hill pictured on screenshot 1 first. Check out the area near the parked vehicles to find a Dog Tag from screenshot 2 (PFC D. Capes).
Go back to the main site, pick up supplies and make your way towards the building indicated by the game. Be cautious, there is another group of mercenaries hiding near it. Given that they're hiding behind the barricade, use grenades to get rid of them quickly.
Explore the rest of the building; you shouldn't run into anyone anymore. You'll come across the last group of mercenaries only after reaching the place where the prisoner is kept. Try to surprise the enemies by attacking from the upper gallery, but watch out for their grenades. When the battle is won, approach the hostage and wait for the mission to end.