^I didn't mean physically. Let's leave the game mechanics aside and just go by lore. Grea fought shadow monsters to protect the academy for a long time and eventually succumbed, but Anne cleared them out with ease. Her magic is simply ludicrous and her summons are all legendary heroes.
Even with her true dragon powers awakened, Grea is no match for a real ancient dragon. Anne is viewed as the greatest magic prodigy in the entire kingdom and she isn't even nearly at her full potential yet.
I'd say if Grea was really quick and got the drop on Anne she could probably end it before the fight can really start, but in a fair duel, Anne has the upper hand.