Gunbuster! (or Aim for the Top!) is a 6 episode mecha OVA and the first work of Hideaki Anno as a director. It focus's on Noriko's fight against the space monsters and her rise to courage. A sequel OVA called Diebuster! was released 20 years later, which is set just before the epilogue of Gunbuster! and stars Nono. The series is excellent and somewhat underrated.
Power of the Verse
Gunbuster!'s power is pretty considerate. Humanity developed technology capable of planet busting and their magnum opus is a black hole bomb capable of destroying a small galaxy. The main enemies, space monsters, can grow to the size of a moon and a nest of them can drain a large star in a few years. Their weakness though is their FTL travel system, which using means that going faster than light makes you younger than those who didn't travel, and many years would have gone by on Earth (this technology in Diebuster! is obsolete). Diebuster! continues the super strength of the series. A blackhole space monster formed from the super blackhole attacks humanity, only to get kicked in two by the main protagonist and her friend.