It's a cop show. Lots of cliches, lots of fun. Kei Matsuba is a growling ex-marine with no social graces and a seventy-year-old voice. (The voice actor is Kenjiro Tsuda, who's just under fifty, but he's doing his usual cool, amused growl and it doesn't fit this fresh-faced young-looking character at all. I think Kei's supposed to be in his mid-thirties.) Meanwhile, Tilarna Exedilica is a magical knight who came here to rescue a fairy. She looks about twelve, but she talks as if she's addressing peasants on the battlefield and is more than ready to use her sword.
They're made partners in ep.1. At first, they hate each other. They'll thaw after saving each others' lives a bunch of times, though.
I enjoyed it a lot, although admittedly it's been years since I last saw a cop show. Watch this show for grumpy cops, awkward lawyers, shouty police chiefs, FBI officials who shove you off your own case and superpowered magic drug zombies that can shrug off bullets. There are hitmen, stool pigeons, undercover cops, prostitutes and pornography. Lots of violence. Lots of sarcastic banter. (Kei and Tilarna are both past masters of the art.)
The fantasy stuff is fun, but not the show's focus. It's colour, to spice up a gritty cop show. We never visit Semaani and there's lots of background detail we haven't learned yet. Kei fought in an Earth-Semaani war, for instance. What we do know, though, is that Semaani has magic, vampires and fairies, but less experience of stuff like guns and technology. (Tilarna's clueless reaction to a porn mag in ep.6 is funny.) There's plenty of metaphor, though. Racism is mentioned a lot. "They don't understand Earth's rules," says a right-wing immigrant-bashing politician in ep.11. "That's why they turn to crime or work for below-poverty wages, stealing jobs and money from hard-working Earthlings."
The plotting isn't the important bit either. It's a cop show, so you expect it to be bitty and episodic. Lots of challenges, leads and confrontations. They might link up, or they might not. There's a bit where a boss betrays a subordinate and you're going "who?" The show had been going too fast to set up that properly... but that doesn't matter.
No, what matters is the characters. Kei and Tilarna are both great fun, while also being real people with dramatic weight and integrity. Tilarna is a small, aggressive fish out of water, ready to cut someone in half at any time. If the world disagrees with her, that just means the world's wrong. She's proud and intelligent, but there's a lot she doesn't know. She can be hilarious, e.g. the porn-and-driving in ep.6, but at the same time she'll also say things that matter. "Don't treat me as baggage!" She's straight-talking and sincere at all times.
As for Kei, he's grumpy and very good at his job. Unlike Tilarna, he understands when violence is inappropriate. Just don't expect a bleeding heart. "So sleep on the ground somewhere. Not my problem." Also, refreshingly, there's no sexual tension between them. They'll get likened to siblings.
Is there anything I disliked here? Well, I'd always skip the theme song. It's quite good, but I dislike Japanese songs that feel they have to swear in English. (Overlord had one too.) I should also note that other reviewers have called the animation bad and cheap. Personally, I didn't notice. The art itself is fine. It's the animation and shot choices that show the budget constraints... apparently. I pass this on for information, in case it bothers you more than me (i.e. at all).
The show works. It's a formula you've seen before, but who cares? I like the characters and I was sufficiently invested in them to find, for instance, ep.7 slightly uncomfortable. (Tilarna befriends a prostitute in a case that's still active, without mentioning that she's a cop. Kei tells her it's a bad idea. Tilarna tells him where to get off.) This is also the show where I first noticed the great Kenjiro Tsuda's voice acting, since which his voice has jumped out at me every time I hear it in anything. The show's both sincere and funny. Recommended.