Top Wo Narae 2!

Adaptation of Top Wo Narae 2!/GunBuster 2
From here
“Top wo Nerae 2! Diebuster follows the story of Nono, a country girl who dreams of becoming a space pilot (or to be more precise, ‘like Nonoriri,’ the meaning of which is revealed as the series progresses) who, due to a chance encounter with an actual space pilot finds herself becoming part of the elite Fraternity. Made up of teenage pilots called Topless, and armed with quasi-humanoid weapons called Buster Machines, the Fraternity’s mission is to protect the people of the Solar System from attack by swarms of uchuu kaijuu (literally, space monsters).
The series revolves around Nono’s quest to become like Nonoriri, her relationship with Lal’C Melk Mark, the first Topless she meets whom she immediately idolizes (to the point of ‘ironically’ calling her onee-sama, or big sister), and the hard work she believes she has to do to be ‘worthy’ of Lal’C’s attention. It also explores her interactions with the rest of the Idols, her efforts to fit in and, ultimately, the truth to her forgotten past.”
The manga covers about half of the OVA story. The “extra story” chapters in Dragon Age are more comedic than the Dragon Age Pure chapters.