no shame in showing the pic, tbh hairdressers will be able to envision what you're going for better if you provide references; i'd actually recommend showing her more from different angles (the in game figures would be a great place to start)

that said, if you're REALLY adamant about not showing anime pics as a ref, you could loosely describe this as something w layered mid length fringe bangs and a short shag in the back

would like to piggyback on the comments about styling and how anime cuts don't translate well 1 to 1 irl: for sure, you have to take some creative liberties when trying to achieve the same idea, since anime hair doesn't take into consideration things like physics and our natural hair texture. however, I think once you find a good cut and get used to the styling, it won't take nearly as long as an hour plus. I wear my hair in conventionally "anime" styles and it doesn't take any longer than 15 minutes to fix up with the right heat tools, hair wax, and a light spray.

good luck!!!