Thanks to Rick B. for this suggestion.
After climbing down into the flooded tunnel near the start of the level...
...turn right, step back a bit, and then use a grenade to destroy the metal barrier.
Now turn around and follow the flooded passageway, picking up the GPS cache (1/3) on the ledge to the left, and continuing around the corner to the right.
Harvest the edible plant at the base of the climbing wall and use a fire arrow to burn the salvage net hanging from the ceiling. Get the salvage and climb the wall to the ledge above.
At the top of the climbing wall, look through the crack in the rocks straight ahead. You should be able to glimpse the relic.
Move in close to the gap, draw the rifle, and click the left stick or press C on the keyboard to adjust Lara's aim. Now you can target a second metal barrier through the gap. Destroy it with a grenade. Then climb back down the way you came and follow the passageway back to the alcove.
Go into the alcove, crack open the salvage crate, and then climb onto the ledge above.
Here you will find a relic (1/2), a Chou Dynasty Helmet.
Return along the flooded passageway to the climbing wall, climb to the top, and squeeze through the narrow opening near the fire barrel to enter the abandoned base.