Trivia: Omicron Persei is actually a real star 1000 light years away from earth.
Trivia: This episode has a couple of nods to Sci-Fi movies. In the initial attack on Monument beach, the Omicronians destroy the White House the same as Independence Day. Later, Fry is wearing the same helmet as the Rebels in Star Wars, and the Planet Express ship goes by a turret that is copied from the Death Star's turrets.
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]