In the "Kill Bill" series, there is no direct conflict or specific event depicted between Hattori Hanzo and Bill, the main antagonist of the story.
Hattori Hanzo, portrayed by Sonny Chiba, is a retired legendary swordsmith living in Okinawa, Japan. In the story, the character Beatrix Kiddo, played by Uma Thurman, seeks out Hattori Hanzo to request a custom-made sword for her quest for revenge against the Deadly Viper Assassination Squad, led by Bill, played by David Carradine. Hanzo initially refuses to create a sword for Beatrix because he has sworn off creating weapons for killing, but ultimately changes his mind after learning the reason behind her vengeance.
While Hattori Hanzo and Bill are both central characters in the "Kill Bill" series, their paths do not cross directly, and there is no significant confrontation or backstory depicted between them within the narrative. Their roles in the story are separate, with Hanzo providing Beatrix with a weapon to aid her in her mission to confront and defeat Bill and the Deadly Viper Assassination Squad.