In this guide
First phase: make the weapon chain miss
Kuroki's first phase mixes high and low bladed attacks in a chain. Trying to stand inside that sequence gives you several timings to survive before you can answer. Start beyond its reach and invite the chain from there. As the last strike passes, close the distance for a short counter, then make room to read the next sequence.
Do not assume the first pause is the end. She can add another strike to the chain. If your counter keeps getting interrupted, wait one beat longer and use a smaller opening. The goal is to trade a safe, repeatable punish for her extended sequence, rather than rush every apparent gap.
Second phase: respect the throw and dash
The second phase changes the distance problem. Kuroki can leap away and throw kunai. A glint on her weapon signals a long-range dash, and the dash may follow a throw. Avoid or parry the incoming attack, but keep watching her after the projectile; treating a successful first defense as the end of the exchange can leave you open to the approach.
If you have unlocked Weapon Catch, it gives you another answer to the thrown kunai: catch and return one when it is safe. A follow-up throw can make an instant return risky, so read the next action before committing. You can still win by defending the ranged attacks and taking the openings you recognize; the skill is an option, not a requirement for this plan.
Work toward a lower-age clear
Use an initial clear to learn the two rhythms. In updated PC and console versions, the Training Room lets you practice against a boss after you have defeated that boss in the story. Repeating the encounter there can help you recognize the end of the first-phase chain and the second-phase glint without replaying the entire Museum each time.
For another Museum attempt, improving the age at which you finish an earlier mission can lower the age at which you start the following mission. That gives you more room to work toward a younger Kuroki clear, although it does not replace learning the fight.
Defeating Kuroki and sparing her are different choices
Taking the normal second-phase takedown defeats Kuroki. If your goal is to spare her, let the first takedown prompt in that phase expire. Break her Structure a second time before her health runs out, then choose the spare option. Sparing her awards the Water Talisman and contributes to the ending route that asks you to spare all five bosses.
For the story meaning of that choice, read the Sifu endings guide.