Howl's Demigod

Anthea "Thea" Grace was the twin sister of Jason, Hero of Olympus and former praetor of New Rome, and the younger sister of Thalia, Lieutenant of Artemis. That was before her brother was given to Lupa and she was abandoned to their mother by Thalia, before their mother died in a car accident when she was seven, leaving her to live on the streets and fight off the monsters alone.

Developing her own technique, Thea managed to survive until she was nineteen. That was when she came across a particularly nasty Arai bearing the curse of a witch to be forever separated from her home, sending Thea into a world with wizards and sorcerers, a world at war.

With no monsters in sight and years of experience on the streets, Thea fits into the new world like the right piece of a jigsaw puzzle, hiding in plain sight and working as a cashier and cleaner at a hat shop. She lives quietly until she runs into a wizard on the streets and helps him escape his pursuers, unwittingly launching herself into the greatest adventure she could hope for in this new world.
Howl's Moving Castle is owned by Studio Ghibli and Hayao Miyazaki.
While I'm using my own character, the Percy Jackson universe belongs to Rick Riordan.
Sorry if some of the lines I take from the movie aren't right.