There is a total of 26 Kappas on the map. Category doesn't require you to do any extra quests other than completing 6 sports to access all Kappas.

1. Archery - There is one Kappa in the archery section of the map. (1)

2. Skateboarding - There is one Kappa in the skateboarding section of the map. (1)

3. Climbing - There is one Kappa in the climbing section of the map. (1)

4. Swimming - There are two Kappas on the mainland part of the swimming section of the map + one on the island and two in front of Green Team headquarters. In headquarters, there are 18 Kappas (Including the leader of the team). To access the whole headquarters you need to get any 6 scrolls. (23)

To make it easier for you, use the map that we've created for you: https://www.speedrun.com/island_games/resources