The jewels can be found on floors 0, 40, 60, 80, 120, 140, 160, 180 and 255. They will be found randomly in rocks. Each jewel can only be found once on the selected floor.
Alone, the jewels do nothing, but if you collect all 9, they combine and the Gem of the Kappa, which helps you regain fatigue when equipped.
The easiest way to get these Kappa Jewels is to save before entering the floor with a Kappa Jewel. Go down to the room using the stairs and start to hit rocks. If you are having troubles finding the jewel and are using a lot of stamina, revert back to your old save. That way, you save yourself the energy, and the floor will be reloaded when you load up your save.
Unfortunately, it is randomized. Even when saving and reloading on the same floor, the Kappa Jewel will appear in a different rock then it will before you reloaded. Just keep trying, and you will eventually find the jewel.
Unlike the other jewels, Kappa Jewels cannot be thrown away, Make them easily identified once found.