In Tsuta Ruins, Blockhead divides a significant portion of the dungeon, forcing one to go all the way around floors 1 and 2 to be able to reach the triple Devil Gate room. Completing these gates and destroying the poison pots is the only hard requirement for obtaining Vine. In all NG+ categories, there is a way to skip this first segment of the dungeon by going more directly to the triple gate room.
In NG+ Any% and All Brushes
Upon entering the dungeon, one can immediately use mid-air KT's to reach the rejuvenate-able bridge on F2.
It's possible to save a KT by clipping through the bottom of the broken bridge collision. This is called Kinnin Clip. See https://www.twitch.tv/videos/610440187?t=1h0m1s.
In NG+ 2017
Without mid-air KT's, it's impossible to directly go up to the same bridge. Instead, you can use a liquid KT to reach the statue in the center of the dungeon, then slope KT up to eventually reach its shoulders. From there, you can simply jump down to the ledge outside the room with the origin mirror before the triple gate room.