Urusei Yatsura(1981)

Urusei Yatsura

It all begins when aliens invade and threaten to conquer the Earth! However, one member of the human race is chosen at random to duel the aliens and save the planet: Ataru Moroboshi, a lecherous slacker from Tomobiki High School who begrudgingly participates. All he has to do? Play a game of tag and catch Lum — the beautiful alien princess in a tiger-stripe bikini — by the horns. Unfortunately for Ataru, it’s not so simple, since Lum can fly and deliver electric shocks! Perseverance pays off, but once he catches her, Ataru experiences another shock: He’s now Lum’s betrothed “darling” and she isn’t going back to her home planet anytime soon!

(Source: Crunchyroll)