To solve the three musical puzzles in Melody Bay, you need to interact with a poster on Frogfucius’ Island. Save Dyna and Mite from the Mines in Moleville. And for the last interact with a Starslap inside a house in Monstrotown.

When you first enter Tadpole Pond, you can head straight to the grey stone switch.

A tadpole will appear and welcome you. Mario will be demonstrating his jump here,

then Frogfucius (along with Lakitu) will approach you.

The tadpoles will swim and form a bridge so you can head to Frogfucius’ island. Walk over and speak to him. He’ll tell you and Mallow what’s currently happening

Once you notice that Frogfucius is standing alone by the edge of the island, approach him and speak to him once again. This is where you’ll be handing him the Cricket Pie from your inventory.

Make sure you interact with the poster on this island so you can unlock the first puzzle.

As a token of appreciation, he’ll give you the Froggie Stick that Mallow can use as a weapon. Also, check the poster on the island before you head out.

Mechanics of Melody Bay

You will need to jump on eight tadpoles to make “songs” to inspire Toadofsky. The key is to jump on them at the right time so they can give the right note. In exchange for every successful melody, you’ll be receiving cards that you can use to access the Juice Bar, and then eventually, discounts and new items at the Juice Bar.

What if you miss a note? Well, you can always start over after you jump on all eight tadpoles. The timing can get a bit tricky at first, but with Super Mario RPG, once you get a hang of things, you’ll be acing stuff quickly.

Also, you can return here after doing the required stuff to unlock each puzzle, but you can also finish all of the requirements so you can do the puzzles one after another. There’s really no wrong way to do them, especially if you’ve done the pre-requisites. Just simply exit the Melody Bay area after you’re done with one puzzle, then re-enter so you can do the next one.

First Melody – Frogfucius’ suite #18

You can access the first melody puzzle when you check the poster on Frogfucius’ island.

Here is the right order of tadpoles:

Second Melody – Moleville Blues

To access the second melody puzzle, you must first rescue Dyna and Mite  in Moleville.

Here is the correct order of the tadpoles:

Third Melody – Monstro Town Star Song

In order to access the third melody puzzle, you need to locate and interact with the Starslap in Monstro Town.

Finding the Starslap

When you arrive at Monstro Town, head to Monstermama’s house.

You’ll notice that her home has a second floor, head up there.

Go upstairs

You’ll see a Starslap—go ahead and interact with it.

Interact with the pink star it will dance and sing for you. Now, you can head back to Tadpole Pond.

This is the right order of the tadpoles:

The Juice Bar

You can access this as soon you get the Alto Card. Head to the western part of the Tadpole Pond, and talk to this tadpole on the right.

The Alto Card will allow you to buy Froggie Drinks and Elixirs.

When you get the Tenor Card, you’ll be given discounted prices on the first two available items. You’ll also be allowed to purchase Megalixirs./

And finally, the Soprano Card will give you an even bigger discount on the first three items, and this time, you can purchase Kerokero Colas as well!

The items you can get from the Juice Bar

Here is the article form Rose Town Walkthrough