Might this be After Transformation, Mine and Her Wild Fantasy...?
When other people experience a body transformation, it is inevitably either male to female or female to male.
Me? I wake up to find myself transformed into two different bodies.
Both a male body and a female body, one conscience operating two bodies, all sorts of embarrassing moments.
Walking together normally makes other people think that I am sweethearts with my other-self, such sadness.
Also, the entire business of a hero rescuing the beautiful maiden, I call Bull.
I get slashed by a sword and my female body gets abducted, and he wants me to thank him?!?! Can it be less of a tragedy?
This is a manhua, and the story begins with someone waking up inside two bodies; one male, named Tyre, and the other female, named Lunaria. There's an academy in the story, named Avalon Academy, and Lunaria studies magic, while Tyre is trained in swordsmanship by a large crab named Kamin, which could be the beast you mentioned. Both Lunaria and Tyre also take part in a few tournament-style competitions, although I didn't see a match where they fought each other. I wonder if you might be misremembering that part.