She trains Yusuke in the Spirit Light Wave Fist (Reikou Hadou Ken) aka the Spirit Wave in the English dub and coaches him to the extreme. Though she may appears nasty towards Yusuke and the others, she truly cares about all of them, and tries to lead them down the right road.
Genkai is an elderly martial arts expert who lives alone in a very large temple. She first appears during Yusuke's second case as he infiltrates a tournament she is holding to find a successor to her techniques in search of the demon Rando. Genkai is a legendary reiki master, known both in the human and demon realms. Yusuke ends up winning the tournament, defeating Rando in the process, and is taken on as a student by Genkai.
Although Genkai is of advanced age and her physical and spiritual strength had gone down, she is still a fighter to be respected and feared. Even after she gave up most of her power to Yusuke, she still is capable of using some Reiki notably during the Chapter Black saga.