From the starting point, after you kill the cobras and get the Medi Pack, walk over to the left side of the tree that is against the bank of the river. You can see a sloped block nearby, which is against the wall and its front side is leading to the water. Stand to the left of the tree several steps away from that block facing it, angle Lara a bit to the right and make a standing jump towards it...

... so as to grab its edge. Be careful though from where you jump. If you are too close to the block, Lara will jump over it, slide down its other side, fall in the water and die. Now, press forward, but just as Lara begins to pull up...

... press Jump to make Lara jump from the block, and as soon as her feet fly off it press Action to make her grab the edge of a branch above and ahead (if you press Action too early, Lara will fall in the river). Pull up to the branch. Now you can seek the items on the tree branches as described in the Treetops section almost at the beginning of the level and then return to the first branch and go to the left, to proceed to the waterfalls.