To enter the Deku Tree from Kokiri Forest, see Deku Tree ยง Entering Deku Tree.
To escape Kokiri forest without beating Deku Tree, see Forest Escape
This is not actually a clip, as there's no collision on the underside of the bridge.
See Quest Oddities for more information on the effects of obtaining Zelda's Lullaby early.
It is possible to skip Mido (who blocks the entrance to the Deku Tree as a Child, not the exit out of the forest), allowing you to skip obtaining the shield. However it is quite difficult to achieve.
Fast sidehop movement after climbing the vines to Lost Woods shown below.