You will come across green ooze puddles on the ground and you will need to use the shovel to aggro them. When you kill them, they'll drop a stunned version of themselves which you'll have to pick up and carry to an NPC called Ooze Farmer. While carrying the ooze, you will lose half a heart at regular intervals. This also puts you into combat so beware of the temporary movement speed reduction when doing jumps. Having healing potions are a big help if you don't want to rush it. Dodging will cause you to drop the ooze. Taking teleports will remove the ooze entirely causing you have to start again. Except for W1Z1 and possibly W1Z3, there's a way to backtrack if you mess up. You can do this on infantile mode and still get credit.
W1Z1 Ooze: Area where the beedogs go
W1Z1 Ooze NPC: In final area to the south up the ramp
W1Z2 Ooze: Skip the worm shortcut and it's just below the next checkpoint in front of the shop
W1Z2 NPC: Right before final checkpoint. Face checkpoint and turn around to see it.
W1Z3 Ooze: I think it was after the second checkpoint in the middle of the area before the checkpoints to the next areas upper and lower paths.
W1Z3 NPC: Take the checkpoint for the upper path and the NPC is on the branch after the leaf part. For some reason it wasn't giving me achievement progression despite having the ooze. Could be bugged. Got it to work on the 3rd attempt.
W2Z1 Ooze: After crossing the flowing river with the log you'll hit a checkpoint. It's to the right after this.
W2Z1 NPC: A pain to get to. You have to do the entire JP climb to the top of the waterfall as the portal removes the ooze. There a food item at the top to restore all your HP. You also need to successful jumps across the logs as they fall to get to the other size. When you hit this checkpoint, you want to use a ledge to the right to jump onto the platform with the flower above. This will launch you to the plateau where the NPC is which overlooks the flowing river.
W2Z2 Ooze: Underneath the building with the rolling gong puzzle. You can take the shortcut eagle and jump off after the 10th group of birds to save time.
W2Z2 NPC: You have to backtrack to the checkpoint that you reached after the second octo puzzle. This means jumping from from from small platform to small platform until you get to where they're too high and you'll need to use the clouds to your right to get back up top. There's a path on the clouds to the right there which you can take with the hut along the way to the right which has the NPC.
W2Z3 Ooze: Difficult to miss. It's after the 3rd checkpoint I think just before you have to climb the inside of the mountain.
W2Z3 NPC: After the climb up where the next checkpoint is. I'd bring HP potions for this.