Kappa lives by himself in the lake on Mother's Hill. He's very anti-social and he'll only make an appearance if you throw a cucumber into the lake's waters. Even when he does appear, he'll scold you and submerge back underwater.

If you throw Kappa a cucumber for 10 days, he'll appear and give you the special Blue Berry with the hope you'll leave him alone. The Blue Berry will help you work in the rain and not become exhaused as quickly. You can throw cucumbers into the lake during Spring, Summer, and Fall. When the Winter season arrives, the lake water freezes.

Kappa is a quite little character in FoMT, but in FoMT For Girl, he is a potential husband :) Just like FoMT has the Harvest Goddess as a special wife, you can complete the requirements necessary and then marry Kappa.