Jungle Hard Shortcut
When MMAN2 discovered this, he called it the "Jungle Insanely Hard Shortcut". I hope to justify the name change.
After the big slide at the start, go left and jump and pull up to the triangular shelf. Walk to the wall, step back once and turn left. Jump forward; if your angle is correct, Lara will land half off the ledge.
I suggest a save here. Do a continuous 90-degree+ left turn (if she pops back onto the shelf, load the save). Now hold Shift and Forward; Lara will slide along the edge! Stop at the position shown, save again, and turn back the other way.
You're almost ready. Turn left to the angle shown, and slide forward a bit so Lara's shadow is at the position in the overhead look in the video. Save again. Press Jump, followed instantly by Forward and Right together. She lands on the shelf beyond the slope. From this position I was successful 10 times in 10 tries.
To complete the shortcut, turn left and run to the wall. Turn left and run forward to drop through the foliage; you land on a high shelf. Run around the corner to the right and do a curve jump around the wall block ahead. You'll see a tiger below.
Note there are no bugs in this shortcut. I don't know if it can be faster then the treetops route.