As the descendant of a monster from the Classic of Mountains and Seas, famous in the Flower Kingdom, she is forced by an accident to leave her parents and go to an unknown world.
She lands in a city in M Country notorious for having the highest crime rate (though the heroine doesn't know that), and is lucky enough to be taken home by a good person.
Their relationship isn't very friendly at first, but thankfully things improve after that.
Basically, an accident in the heroine's original world leads her parents to send her to another world. She uses up all her demon power and turns back into her original form, whereupon the Old Master finds her and takes her home (to study her). He later adopts her, and along the way she helps him raise four little birds.
The pairing might be, uh, and I said might, Jason AKA Red Hood AKA the second Robin.
Mainly DC, though she might travel to other worlds.
