Yuugeki Uchuu Senkan Nadesico

An alien armada from Jupiter has amassed enough power to destroy all of Earth’s defenses. Earth’s final hope lies in the Space Battleship Nadesico, a ship created using recently discovered extraterrestrial technology. The Nadesico’s rag-tag crew must overcome their idiosyncrasies and defeat the alien fleet or Earth’s last hope will be lost.
(Source: AnimeNewsNetwork)