Unless Tifa used a jutsu to replace herself with a log, she is still a human being being slashed from top-down. The force would throw her head back and that alone would cause her hat to at least fall to her back before she went flying down the stairs. I stick with the idea that she tied her hat on tight before confronting him. She did have to charge pretty quickly up those stairs.

Then again, the way she kind of hunches beforehand, her hat should have fallen at Sephiroth's feet. In fact, she kind of hunches before the slash so Sephiroth should have taken, like, half of her face off.