two rounds. One on Onigashima and the other on mount fuji.
On onigashima, Big Mom betrays Kaido, and is able to get a giant slash off on him with napoleon. Somehow, big mom learns the truth about Mother carmel and goes into her crying/defenseless state. With her will broken and her defenses down, Kaido is able to easily knock out big mom and her crew.
The alliance is easily able to take out most of the beast pirates, including both the numbers, the tobi roppo, and most of Orochi's subordinates. However Orochi, the calamities, and kaido still haven't been taken out.
Seeing themselves outnumbered, they retreat. Or at least that's how it appears. From the poneglyphs of Onigashima or perhaps from yamato, we learn that the ancient weapon Uranus is actually located at the peak of Mount fuji and that Kaido is attempting to use it to destroy wano and after which he will use to wage war on the world.
Big Mom creates some homies which transport Luffy, Law, Kidd, the m3, Drake, Momonosuke, hiyori, usopp, and Yamato to mount fuji where they face off against Kaido, the calamities, and Orochi.
Kaido is ultimately defeated when Luffy is able to momentarily immobilize him, allowing the alliance to redirect the power of Uranus(which I suspect is like some sort of a death star) onto Kaido, ultimately killing him. Kaido dies but not before having a moment with Yamato.