The battle with Lady Butterfly is one of the earlier boss fights in Sekiro: Shadows Die Twice, but that doesn't mean this boss is a pushover. Lady Butterfly is probably the fastest enemy players will have faced by this point in the game, and she requires you to learn a lot about deflecting enemy attacks, anticipating multiple threats, and using all the tools at your disposal to strike at the boss and do damage in order to eventually take her down.
You'll find Lady Butterfly at the end of the Hirata Estate level, which you can access once you locate a particular old woman in the Ashina Outskirts area. Talk to her and she'll give you an offering bell you can take back to the Dilapidated Temple; give it to the Buddha Statue near the Sculptor, and you'll be transported to Hirata Estate, and three years into the past, to see the events that unfolded there. Getting to Lady Butterfly is a long, tough fight, but quick reflexes and the right Shinobi Prosthetic tools can help make quick work of her.
Lady Butterfly employs apparitions in her fight, which is why Snapseeds are extremely useful to bring with you. You'll get one of these consumables from a wounded samurai just outside Lady Butterfly's boss room, and we've got a handy guide that will help you find more, as well. When Lady Butterfly summons her ghostly apparitions, use the Snapseeds to dispel them--just make sure you're close to the ghosts, since Snapseeds are only effective in a radius around your body, and they won't work if you're too far away.