#1. Once the mission starts, continue following the path until you found the first group of dismembered marines. Continue forth until you spot an enemy drop ship. Stay out of sight then continue forth. Look at the sheet on the ground to find the first dog tag of the mission.
#2. Get past the ship wreckage and fight more xenos. Push forward and look for a green cache to the left, before entering the tunnel. There's another dog tag there.
#3. After reaching the room where Oneal downloads the personnel manifest, find the dog tag on top of the console that he's working on.