Mizuki is a friend of Yukimura
She is first introduced in a flashback in volume 11. Her main desire is for her father to not be as protective of herself and her mother; it's strongly hinted that she and Yukimura were falling in love with each other. Yukimura promises to protect her, but that same evening Tokugawa attacks the city and Yukimura is unable to save Mizuki, who gives him her father's sword before dying in his arms. She correctly predicts that he will become much stronger and that there are people who need him.
Her death prompts Yukimura's inner "dragon" to awaken and turns him into a fierce "demon" who punishes evil. Even twenty years after her death, Yukimura and Saizo still mourn her and Yukimura still carries the sword she gave him.