She uses the Breath of Love (恋の呼吸 Koi no Kokyu) which is derived from the Breath of Flames (炎の呼吸 Hono no Kokyu) and her instructor was Shinjuro Rengoku the former Flame Pillar
Demon Slayer: What is Breath of Love and why is Mitsuri Kanroji the only user? The Breath of Love is a breathing technique that was developed by Mitsuri Kanroji herself.
Mitsuri's reason for joining Demon Slayer Corps is Unique As we know, Mitsuri Kanroji had a unique and powerful muscle system. Her strength was a supernatural phenomenon on its own. However, with such high muscle density, the body also needs an equal amount of food to maintain itself. Thus, her diet was much more than any normal human.
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what breathing style does mitsuri use