Mobius Dick - S6-E21
Trivia: Amy's mother says, "My days of joy and luck are over. Guess I have to leave that club." This is a reference to the novel "Joy Luck Club," the film adaptation of which starred the voice actor for Amy and her mother, Lauren Tom.
Answer: You are thinking about episode 20 of series 2 - "Anthology of Interest I". She technically never kills anyone, but in the episode she ask a "What if machine" (one of the Professor's inventions) what would happen if she was more impulsive. The machine then shows the more impulsive Leela killing off the Professor to get the money from his will and thereafter killing Hermes, Bender, Scruffy, Cubert, Nibler, Amy and Zoidberg to cover it up. Finally she does something really impulsive with Fry.
Andreas[DK]