Here's my two cents:
I don't care. The way you're telling the story doesn't connect with me as a reader. I find it difficult to care about the main character. I think it's because of your style, it's pretty distant and cold. "The woman, Asayu," is a good example of this distance and coldness, why not simplify it to just her name? I already know she's a woman, you just told me in the first paragraph, pointing it out again creates redunancy.
You point out that the main character isn't human, but you don't really explain in what way. Is she an alien, a magic being, a bit of both, something else entirely? She looks human, acts human, but isn't. Using the word "Earth" is another example for me of creating that distance, three times in one paragraph to point out that the otherwise human character isn't human.
Wait who is Rachel? Oh wait, doesn't matter, she isn't mentioned again.
And this is where I complete lose the direction. You throw in that a cabal of mages has placed some sort of spell on the village and its inhabitants.
When she is medidating, is she confronting the effects of the spell? It seems like it, but a couple of lines later you again have her arm herself against the effect, but without succes, but after a while the effect fades and she seem able to ignore the effect. Is it because she armed herself against the effect or because the monkeys startled her and the shock released her from the spell?
So she disrupts the ritual, shoots someone, and flees. I'm left wondering why did she disrupt the ritual? She assumes it's an evil ritual but there's nothing to go on. She assumes the villagers are the intended victims, but they aren't, does she know these mages? Is there a history there? Who are the mages anyway, what is their goal? Why should I care about Asayu kicking these guys down? What master do they serve, what master does Asayu serve?
I think the idea you have is a solid one, but you create a distance by using words and syntax that create distance. You want to paint a pretty picture but you end up trying too hard. Pick words and a structure that is a bit less dramatic.
Give us more insight into what the main character is about. You want to keep her origins a mystery at this point, no problem, but make her more mysterious by removing the references to her appearance. Make her a true mystery by only giving us a glimpse of her origins.
"This place has different rules," she whispered to herself as she studied the gun in her hand.
It's a bit more subtle to suggest she's not from around here than pointing out she usually fights with a stick and she's not native to Earth. If you want to keep her origins vague, make sure you avoid giving us too much details. If you want to give us the general story, make sure it's well-rounded.
Asayu studied the gun in her hand. A wayward soldier had surrendered the piece to her on her first mission and she had been using it ever since. A complicated weapon for such a simple world,
she thought. In a twisted way it makes sense.
In a nutshell:
Don't try to create elaborate sentences that swirl around themselves. Sometimes it's best to keep things simple, because by keeping it simple you can create a more down-to-earth atmosphere that is easier for the reader to relate to.