It seems our Wiggler segment got itself stuck to another web. The comet piece is here, but it's out of reach. There's a door drawn near the entrance to this area. The Secret Door leads to coins and the Tape. We go to the right to the next area. We have to cross a large web, so don't jump on it too much. Towards the back, it gets foggy. The sign in the area says the fog is coming from the nearby poisonous hot spring. The Snifits seem to be enjoying it. Go up the ramp to the tree and get to the other side of the web. You can go over the blocks, but using your hammer here will make Scuttlebugs descend to battle you. The path dead-ends at the next tree. Drop down through the web and continue to the first area, to the left.
We can now free the Wiggler segment. This one's also itching for battle. Kersti says the segment's too old for shenanigans. It has 15 HP like last time. After being defeated, it, too, is remorseful and follows us. We go up the steps to the right to find the other Tree Stump scrap. Go to the area to the right and cross the poison pool on the right side of the tree. Go through a doorway to the left to find an HP-Up Heart. Since we can't find a way to the comet piece, we look around. We go near the Hot Springs and the segment hops in and soaks, until it gets too hot. Go up the ramp and drop down where the web was, then walk to the back. You'll see the same area from behind. This will give us access to the ramp to the comet piece. This opens the path to 3-2.
After you clear the poison, in the first area, near the entrance, go into the dried-up pool to find the Watch Battery.