Don’t just climb up and cling to the vines.
Climb to the top, and cut 2 blocks out under the top of the tree. Stand there, and put up blocks if needed. Zero danger.
Climb up and break leaves, until you can access the treetop. In that jungle there’s nothing but trees around and they are very very tall. You’re safe from everything except tornadoes. Hop from tree to tree and leave the mobs behind.