From the steps, which used to be the slope where you entered this room, you can see the artifact at the top of the broken flight of steps below the second metal ring. That's where you're headed.
Hop down to the second step from the top and take a running jump to grapple the first ring, above on the left. Adjust the cable length if necessary so Lara's feet are just above the line between the carved and plain sections of the wall.
Wall run back and forth until Lara is running nearly all the way to the far corner. Then, the next time she swings that way, jump back off the wall . . .
. . . and quickly grapple the second ring on the underside of the ledge behind her.
If you're doing a time trial or just don't want the artifact, don't drop down. Instead just swing to the right, jump and grab the corner ledge.
To get the artifact, slow your swing until Lara is hanging by the cable above the step with the artifact. Swing just a tiny bit to the right, so she's directly above the step, and press Crouch to drop down. Collect ARTIFACT #2.
[Return to the Obelisk of Khamoon Walkthrough]