So the g/f gets Supergirl and, by proxy, I too then get it and read it.
It's quite good. Of the New 52 titles, this Catwoman, Batman & Robin, and Flash are really the only ones that seem to be worth reading, though I'll be sure to grab Nightwing in trade once it comes out.
Supergirl is interesting because they've really gone out of their way to completely alienate her. She housed Superman himself in only the second issue (her own cousin, which she still doesn't believe), then she flew all the way back to where Krypton Was only to discover it had been totally destroyed.
There's World Killers apparently. Five of them, born of Krpytonian Science and their embryos have origins from multiple worlds across the galaxy, and one of them was Earth.
Well, Supergirl may not understand Earthlings yet, get what she's doing here, but she remembers her father and what he stood for, her Uncle Jor-El, and she knows 5 people of incredible strength shouldn't be allowed to just pummel a planet. So she pummels back (with awesome backstory flashbacks to fill in the fighting sequences).
7 issues later it's obvious, there's only 4 Worldkillers. Where's #5?
My opinion. It's Doomsday. If you think about it (and apply the clues from the Supergirl comics) it adds up the right way. Perhaps.
Anyways, who else has read this?