You will eventually come to a crate and pool of water. Drag the crate back to the left, underneath a hanging rope. Use the crate to reach the rope, and swing to the right. You need to create enough momentum to allow you to jump off and reach the right-hand branch.
This is the first real platforming section in Limbo.
From this branch, jump to the left and follow the branch to the other side of the tree. Jump to the next one on the left and then across to the right. Continue jumping rightwards until you reach a split tree. Push the tree so that the top half breaks off and falls below. Do not jump down yet, as there is an achievement to be had.
From the branch leading to the tree you pushed down, jump to the left as high as you can. You should grab onto a rope. Climb about halfway up, then gain some momentum so you can jump to the left and reach the hidden section with the achievement egg inside.
Achievement unlocked: Altitude is attitude (5G)
Drop back down to ground level, using the branches to get down (or you will die from the fall).
Get this tricky achievement
Once on the ground, push the crate to the right. It will knock into the log. Push both into the water – as far in as you can without risking drowning. You can then use these objects to cross the river and get to the bank on the other side.