This is a traditional to the First Years. We always have them compete with others who have managed to move into Atlas Academy while the Faunus hopefuls can join, in order to test out their skills in combat. But these do come with alternative motive in the end.
We would normally have at least four to eight fights, but also these fights are usually to determined who's fitting as a Captain of the teams for the Humans. And if there are some Faunus that had managed to win or even impressed me, and survive the Battle Royale, they're likely to be named as Team Leaders. More like a performance evaluation, to those who did managed and willingly to show their intention to lead or be the best.
There is something that both Atlas and Shade Academies had in common, is that we believe iron sharpens iron. Shade wants to best to survive the environment, but we believe in finding the best from competing against other Hunters.
Fighting Grimm is nothing more but mere child's play. If an untrained civilian claims to kill Grimm before, then what's the point of having an Academy on facing such borish creatures. So fighting each other in order to improve their skills as a Hunter, is a far more efficient way.
You can tell through these battles on what to do with the acceptances, and the those that got through by dumb luck. We reward those who had proven their worth while those who had gone by will be challenged, regardless if they're Faunus or not. So don't disappoint.
As for how to determined the battles, it's more of a open challenge to those who want to compete. Even the Faunus hopefuls can accept, and accept only due of them not being Academy students yet. But this does got a cost, and no, not like paying a fee or any kind of payment. The cost is being scouted out by their other Faunus rivals that wanted to be accepted into Atlas Academy, thus they're normally been targeted by others due of how powerful they are. On the other hand, there are some Professors, and myself, are looking out to those who seem promising. And also the high society will make wagers in those gambling spots, and increase their chances.
So good luck to all who want to compete.