At the end of the tunnel leading into the base from Shipwreck Beach, jump across the deep shaft and latch onto the climbing wall.
Climb down as far as you can.
Then drop past the section of chain-link fence to the bottom of the tunnel.
NOTE: You can drop past the fence and latch onto the wall below, but this isn't necessary, since Lara won't take much damage dropping from the wall just above the fence.
Turn right, step back a bit, and then use a grenade to destroy the metal barrier. If Lara takes a little shrapnel during this process, wait for her to heal completely.
Then use another grenade (or an explosive arrow if you've unlocked this upgrade) to blow out a second metal barrier inside the alcove, above on the left. It's difficult to get a good angle here, so Lara will probably take a little damage. If she starts with full health, it won't be a problem.
Or, to avoid taking damage, try the slightly longer alternative strategy described on this separate page.
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.
Drop down and exit the alcove. Wade through the water to the ledge ahead on the left to find a GPS cache (1/3). Then continue along the flooded passage as it takes a U-turn 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.
Then squeeze through the narrow opening near the fire barrel to enter the abandoned base.