The river of poison circles an island with a scrap on it. In the next area, we can see the comet piece, but can't reach it. There's a door drawn near the Boomerang Bro. It leads to the Pillow. We go through the tunnel in the back. There are coins floating over the river. We ignore them and go to the right. Here, we see another comet piece and a Wiggler segment fast asleep. We can't reach them from here so we backtrack to the area with the other comet piece and go to the right. We can't reach it from there, either. Kersti mentions floating down the river on a leaf might be relaxing, so we go back to where we found a tree with a leaf and hit it with a hammer. The leaf falls into the poison and we hop on. When going around the front where the scrap is, jump between the bridge and the island for three invisible blocks. Paperization doesn't reveal much besides a door drawing. Then, I figure it out: when on the leaf, you can jump to the land close to the screen in the area where coins float over the river. There's some Bowser tape holding back the ground that lets you through the tunnel to Wiggler's segment.
It then battles us. It has 15 HP. A Boomerang takes it out easily. The Wiggler Segment seems sorry and follows us again. The comet piece is nearby. The path to 3-6 opens up and we can see a snowy area across the water. Kersti says we should take the segment home. I agree.
Once we return the segment, we go past the comet piece we collected to the other tree with a leaf and hit it into the poison. This leaf is closer to the back wall, so once we float alongside the edge of the area where the Bowser tape was, we can hop off onto land. We can now go outside to where the Piranha Plant is and jump on the invisible blocks to the scrap we couldn't reach earlier. It's a Tree Stump that was missing from Wiggler's house. Go inside to get the comet piece, which opens the path to 3-2.