It's an OVA series: Queen's Blade: Grimoire (quite good, although only two episodes and of course as sleazy as ever)

I hated the main character. I liked his childhood friend, but he's unlikeable (admittedly by design) and the rest of the cast is mostly annoying too. There's a cool twist halfway through the episode, but that just lifted it from "RUN AWAY SCREAMING" to "could be interesting, but I still want everyone dead".

We begin with aliens attacking the Earth. Mankind responds with missiles, tanks and soldiers. Cities become warzones. Children are getting sent into cold sleep, with one of them promising her friend that there's going to be peace when they next wake up. Everything gets trashed.

"That was the day our world ended for the first time."

Some time later, we meet our hero! His name's Ichiya and he thinks he's the only person in the world who matters. According to him, he's the saviour of mankind. (The really distressing possibility is that because this is anime, he might be right.) He calls other people "stupid girl", "useless powerless ones" and "scumbag" while saying things like, "Why should I waste time thinking about trivial matters that don't involve battle?" When Canaria chides him very mildly for unfriendliness towards younger students, he says that not acting like a dick "would lower my soul level".

Canaria's the show's only nice character, but she's also clumsy, falls over and has nude shower scenes. She has an alien-fighting superpower, like Ichiya, but it's singing. No, really. She gets a microphone and sings. It wasn't immediately clear to me how this helped.

Eventually we meet other teenagers, distinguished not by their superpowers but by how they're annoying. There are also invading aliens, called the Unknown. I hope the Unknown win.

The twist is that all these teenagers have a rank, indicating how strong and successful they are at alien-fighting. In order to increase this rank, they're liable to start fighting each other rather than the enemy. They'll compete to be the one who takes down an alien, or even perhaps just shoot each other. Admittedly that's merely a distraction and I think they're all powerful enough to be able to survive some friendly fire, but even so I'm sure you could cause a fatality if you really wanted, e.g. by throwing off an ally in mid-combat.

This wouldn't mean much if the cast weren't twats. It had to be that way. I get it. Only world-class bell ends would act like that when they were supposed to be defending mankind. Sensible people wouldn't care about their rankings under those circumstances, but that would untwist the twist. I might even have continued with the show if it weren't for Ichiya, but... yeesh. No no no no no. Good grief, he's irritating.