Well, as she refuses to do the princess thing, makes her more looks like a heroine than a princess.

What Sparklefairy said. Plus she hasn't got a Prince, so not a classic Fairy Tale Princess to me.

Uh I guess Merida.

Well, the obvious choice is Merida. She was blatantly advertised as the pseudo-princess.

The less obvious choice is Tiana. Tiana doesn't want a prince or love, either. Tiana just wants her restaurant. It was Disney who pushed the "love thing" onto Tiana. Because Tiana is a businesswoman, she has always seemed less of a princess to me.

She isn't even a princess in the movie, since we never see her get married, and she doesn't feel confined to the princess title. Merida may be an anti-princess but she goes out of her way to act out of the norm that you're constantly reminded that she IS royalty.

the obvious choice isn't merida, it's belle.
she is literally never a princess, or even royalty, at any point during her movie.