Take the side passageway leading to the medlab, but turn left on your first chance, into a corridor that has been previously unavailable (the above screenshot). Move forward. When you reach the part that is destroyed, jump down to the level below. Find the stairwell and go down one level more. Open the nearby door.
Turn left and prepare to eliminate the Xenomorphs coming your way. Obviously, I recommend using the smart gun, which has the advantage on staying on target, but, since it has large firepower and you can't reload it, fire in short bursts only. If you want to spare ammo even more, let O'Neal take down some aliens without your involvement, but don't risk it too much.
Keep moving forward, killing every alien you encounter and trying to keep the smart gun for as long as possible. Look for a room which you can enter, where, apart from a single Xenomorph, you can also find a full set of armor and the above Dog Tag (PFC Jenette Vasquez).
Go back to the main corridor and resume the move forward. Expect the next Xeno encounter at the fork pictured above. You'll need to be especially careful here because the aliens will come at you from both corridors. It's best to retreat a little so that you could eliminate them from a safer distance.
Stop and at the fork. I recommend taking the left corridor, pictured on screenshot 1, because it's the easiest way to a new secret item. When you get to the edge, jump down to the level below (which means you can't go back to the previous area) and turn around. In the spot illustrated above, on screenshot 2, there is a new Dog Tag (PFC M. Macaulay).
As you make your way to the last part of the base, watch out for Xenomorphs Lurkers. They're much smarter than the regular ones; they can hide and wait for the right moment to charge and perform a melee attack. Try to prevent it any way you can; use the smart gun or any other strong weapon (i.e. the tactical shotgun). As a last resort, be ready to play the traditional mini-game (rapidly tap the interact button). Lurkers let out a characteristic sound, so if you use the motion tracker you can also try to avoid them altogether.
Your current destination is the passage illustrated above. Wait for O'Neal to open the door and move into the next location.
Search the room you'll find in a few moments. Apart from standard supplies, you can also find a Legendary Weapon here: Gorman's Pistol (the above screenshot). Use the welding torch to unlock access to the adjoining area. You'll have a surprise encounter with an overgrown Xenomorph which ends the mission.