How do I get the tadtone located under the lilypad?

To be able to get that tadtone, you need to flip that lilypad over. The spiky side is down in the water so you won't be able to use your whip on it. So if you remember what happened in the Ancient Cistern with the lilypads, to flip it, you need to jump on it from high above. The only way you'll be able to jump on it with a significant enough height would be from the great tree.

It should be pretty obvious where to jump from. When you climb the tree, there will be a part of the platform jutting out in the direction of that lilypad. Go to the end (and make sure you're facing in the direction of the pad) and jump down. You should be able to land on the lilypad, flipping it over and releasing the tadtone.

In order to get these, you have to remember how the lilypads worked in the Ancient Cistern.

You have to go back inside the tree, then exit back out to the branches outside. Once there, you can climb up the tree until you reach what looks like a ramp (which wasn't used your first time through here).

Jump off the ramp onto the lilypad to flip it over.