Begin with a hook. A great way to start is by writing a scene that immediately grabs the reader's attention. For instance, you could start with the Kappa in a dangerous situation, like being chased by some unknown sea creature, and the Castle Swimmer comes to the rescue. Then, introduce the Siren as a mysterious figure in the background. As you write, gradually build the relationships between the characters and introduce the main plotline that will drive the story forward.
First, do some research on each of the elements. Learn about the characteristics of Castle Swimmers, Kappas, and Sirens from their original sources. Then, think of a simple starting point like a chance encounter. For example, the Castle Swimmer could be exploring a new part of the ocean and accidentally bumps into the Kappa who is on a mission related to the Siren. Just start writing down what happens next, don't worry too much about making it perfect at first.
You could start by creating your own unique versions of the Castle Swimmer, Kappa, and Siren characters. Decide on their personalities, goals, and relationships. Then, think of a conflict or situation that would bring them together. Maybe the Siren has lost something important and the Kappa and the Castle Swimmer are the only ones who can help. Begin with a vivid description of the setting, whether it's a dark underwater cave or a colorful coral reef, to set the mood for your fanfiction.