When is the earliest you can have the Level 2 Sword?

There are 26 Secret Seashells hidden in different places in the game's world. When you have at least 20, you can visit a certain location and get the Level 2 Sword.

Each Seashell technically requires the use of certain items to get, either because you can't get the Seashell itself without the item (for example, you need a shovel if it's buried) or because you can't reach the area it's in (for example, any Seashell outside Mabe Village is unreachable without the Power Bracelet).

Without using glitches or other methods to break the game's rules, when is the earliest you can have 20 Seashells?

If the changes made to the DX version make a difference, I'd be interested to know about both of them.

Please note that I'm not simply asking for a list of seashells and what is required to get each; I've found guides with this information but they all assume you are able to reach the location of the seashell and don't list any items you may need to get there.