Go to the end towards the tree trunk and take a running jump to the bent branch on the right.

Stand on the bent part of the branch and turn having the previous branch to the back of you. Take a running jump to the opposite branch without pressing Action or Lara will not make it. Get the Flares from the alcove on the right hand side and...

... take a running jump back to the previous branch (the bent one). To make it, stand on the higher part having the alcove from where you got the Flares on your left and again do not press Action. Take another running jump to the next branch (2) ahead (no Action) and then jump to the branch on the left. Pick up the Desert Eagle Clips and make your way back to the very first branch above the stream the same way you came.