Take a running jump from the doorway to the square ledge in the corner. Grab the handhold on the wall above and climb to the left. Drop to grab the handhold below, climb to the right past the broken section of the upper handhold. Then jump up to grab the solid section of the upper handhold.
Continue climbing to the left around the corner.
When you reach the end of this ledge, lean out to spot the handhold you're aiming for. It's quite a distance below and to the left. Jump to the left, grab and press Interact to perform a saving grab so Lara doesn't fall.
Climb around the corner to the left . . .
. . . and pull up into the alcove with ARTIFACT #3.
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