Moonglow Bay

Certain residents in Moonglow Bay will tell you about strange fish. Talk to them indicated by an exclamation mark (typically by pressing ) and they will inform you about a new fish and where to find them. A message "Fish Updated" will pop up in the bottom right corner indicating the new information in your journal.

Not all residents have unusual fish stories. The ones that do typically have a couple, telling you one every day until you've heard them all. Go around town and talk to each resident to hear their fish stories and repeat for 2 more days and you should have heard enough stories to unlock this achievement. Later in the game, you will renovate the Cozy Cavern where you can talk to Elvice Laurent for even more fish stories if needed. He will tell you 2 stories each day until he runs out of stories.

As commented by Panoramixx85, it is still possible to listen to the fish stories after finding and researching the corresponding fish, meaning this achievement should not be missable.

Let me know if anything is missing or if something can be improved.