Sorry, didn't catch this... Supergirl was never... well, yeah, I guess it could get kind of violent, e.g. the fight with Batgirl (which is awful on a lot of external levels, but would have totally worked if not for all the talking, some of which involves the dumbest words ever written in a comic book: "red wavelength UVB lights"). But afaik she never killed a guy. Tried to kill the Anti-Monitor (and Matrix tried to kill Doomsday), if that counts, which for DC editorial purposes apparently does not. Alien monsters don't have souls. Which you'd think would make killing them even worse, but maybe not.