So far, Supergirl has established that Krypton was destroyed thanks to the planets climate change, which ultimately caused it to implode from within. We dont know what caused these changes; it could easily be that Kryptonians were just as harmful to their environment as we are to ours, but maybe, just maybe, it was Braniac. In many versions of the canon the god-like, Skynet-esque thought-entity has been responsible for the destruction of Krypton, usually for reasons of either finding the world inferior or just simple curiosity. Well, simple curiosity on a ludicrous scale. If Supergirl wants to build up to a really big villain, there's no better choice than Brainiac. Just imagine what Kara would do when the being responsible for her home-world's destruction came to Earth, threatening her adopted home. Losing Krypton was a trauma that's defined much of her life. Unlike Clark, Kara has a far more personal stake in this. She saw Krypton get destroyed, remembers it, longs for it. Remember when Kara went in a grief fueled rage and fried Red Tornado? Take that and crank it up to eleven. Imagine the endgame showdown: Brainiac has come to earth and is preparing to assimilate it for documentation, all the while speaking in a haunting, robotic tone about being the most perfect being in the cosmos. Then the two have an epic final duel, Kara fueled by all the rage of a dead world, fighting at her most powerful.