Satomi gets one simply for being such a Chick Magnet that even the Goddess of the setting has the hots for him. On that note, the fact that he ends up with her.
Volume 1 (Anime episode 1)
Shizuka putting the beatdown on Koutarou and the first four invaders for destroying Room 106.
Volume 2 (Anime episode 3)
After Theia blew up the course, Harumi and Yurika, the two weakest runners, winning the athletic competition.
Volume 3
The Invaders coming together for the first time to save Sanae from the Ghost Hunters and the Ghost Lady. The three leading moments were Koutarou's realization that the "Save Family" charm would be unable to harm Sanae, Signaltin manifesting for him for the first time to ensure that the charm reaches Sanae, and Yurika's magic (unknowlingly) interfering with the Ghost Lady.
Volume 5
The Invaders combining to defeat Maki. The second manifestation of Signaltin, and Shizuka stopping Theia from using her energy weapons because her righteous anger over Maki damaging Corona House trumps space battle weaponry.
Volume 6
Once again, the Invaders combine to defeat the People of Earth Rebels. Yurika containing the explosion at the end, without anyone knowing, probably wins.
Volume 21
Theia burns out the propulsion unit of her control suit to save the life of a loyalist space fighter pilot who attacked them on orders from the Coup d'etat leaders, knowingly condemning herself to death via unprotected atmospheric reentry in the process. Theia is indeed a true princess of Forthorthe. Then Koutarou in the Blue Knight armor and Yurika in an ordinary space suit save her by using Koutarou's controls and Signaltin and Yurika's mana to shield them during reentry.
Koutarou's confidence, and the banter between him and Theia, defuse any real "cliffhanger" suspense, but that just allows the moment to become almost a crowning moment of funny: They streaked through the skies of (the Forthorthian system planet named after) Alaia together, leaving behind a long tail like a meteor and the high pitched sound of Yurkia's panicked screaming.
Volume 25
The crowning moment is the battle in Rumstock Cemetery, where the ghosts raised by Dark Purple to fight Koutarou, Kiriha, Maki, and Clan turn out to be many of the Blue Knight's comrades and soldiers from the Coup in Ancient Forthorthe, who are able to throw off Dark Purple's necromantic compulsion to fight alongside Koutarou once again.
