Minecraft: Story Mode - A Telltale Games Series

Here is a step by step on how to get through Chapter 5:

Defeat the mob outside the portal.
Decide whether to build a hut or a tree house.
Decide whether to give a cookie to Lukas or not.
Decide whether to have Lukas stay or leave.
Climb up the vines.

All credit goes to IGN. After you climb the vines, a cut scene should roll out and the achievement should pop moments later. If it does not for some reason, it will come up at the start of the next chapter.