Take a standing jump from the edge to grab the ceiling grates. Monkey swing across to the other side and drop onto the ledge with the save/power-up crystal.
Turn around, move to the left side of the ledge, and take a standing jump without grabbing to land on the sphinx's head.
NOTE: If you want to go after both the single rocket (or rocket launcher) on the face of the sphinx and secret #3, see the notes in the main walkthrough.
To get secret #3, turn about 45 degrees to the right and walk to the corner of the flat tile on the top of the sphinx's head. You're now aiming for a ledge that you can't see. It's located on the back corner of the sphinx's head, as shown in the screenshot above.
To get there, carefully position Lara so the point sticking down from the ceiling lines up with her left shoulder.
Now take a standing jump with Action...
...and Lara will land on the ledge. Pick up the small medi pack.
Walk to the edge and take a standing jump to the tall, square pillar.
Turn left and take a running jump to grab the back of the angled, white ledge.
Pull up, slide just briefly, and jump onto the long ledge ahead.
Go to the other end of the ledge for SECRET #3—a save/power-up crystal and 2 rockets.
Now return to the middle of the long ledge.
Take a running jump onto the sphinx's shoulder. If you land on the spot shown above, Lara will not take damage. Slide back and grab/release to drop to the floor.
If you want all the kills, take a brief detour over the sphinx's front right paw.
When you slide down to the floor, a guard appears. So run around to the right...
...and take care of him as he approaches.
Then go all the way around to the other side of the sphinx.
A second guard opens fire from the stairway about halfway along the right wall. Kill him and grab his small medi pack. (If you didn't kill the previous guard but did trigger his appearance by climbing over the sphinx's paw, he'll sneak up on you now, so watch out.)
Before climbing the stairs, head for the back right corner of the big room (when facing the sphinx) to find some shotgun shells.
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