Itsuka Shido is a high school boy who, on the last day of the spring holidays, witnesses an explosion that destroys the town with a mysterious girl in armor appearing in the center of the blast. Shido’s sister, Kotori, tells him that the girl is called “Special Disasterous Designated Creature: Spirit”, which causes a timespace quake.
Kotori also discloses that she is the commander of the anti-spirit organization Ratatosk and orders him to go out on a date with the spirit girl. Kotori says, “I don’t ask you to beat the spirit. Just let her fall in love with you and save the world.”
Yep, a harem anime where the male protagonist needs to make various space battle women fall in love with him to beat them and save the world. Enjoy!