So, my recommendation is a special academy built on a hidden island which is protected by a super scifi shield projector built from stolen alien technology. Above the academy is a giant metropolis city where people chosen from all over the world for their specific traits and powers (espers, good athletics, etc your choice but basically skills over everything else) are allowed to live in order to save humanity. The academy is part of this city.
Underground could be the experimental, more evil parts of it, like alien autopsy or illegal cybernetics.
Anyway, the point of this academy is to create soldiers to fight the aliens by using any and all means at humanity's disposal, so to that end, you can have student duels between people who prefer different types of combat.
I-e a cyber enhanced wizard.
A genetically modified living weapon.
A mecha rider versus natural born magic god.
Or the like.
Naturally, you will need to introduce the enemy of humanity somehow to the students. Field trip gone wrong? Maybe captured aliens are made to fight against the students.
One of the more important choices you need to make is how depressive do you want this story to be? Is it a "humanity, fuck yeah" type of story where the aliens attacked but the humans are winning due to 'insert classic human xenophobe reasoning here' or perhaps its a losing war and the expectations of the students are high? Maybe the academy is secretly funded by secret aliens, to fight the different invading aliens?
So, let me tell you about the current planned world a little.
While the academies are open to the public (for propaganda purposes of course) fights between students are planned to happen and yeah the world is kind of in a bad situation.
Cold War is still going even though both sides claim it ended (there are two new factions out there even) Drug cartels and people who abuse their powers lead powerful paramilitary groups, and they have great power because the world is already busy enough with aliens.
There are secretly government-funded labs that work on orphans to create artificial super clone soldiers.
And about students learning about the enemy. Well, humanity is fighting against them for hundreds of year's and that enemy is ironically the reason why humanity has supernatural abilities.
Korean Peninsula, some parts of Japan and China, more than half the South America turned into a wasteland after a war against aliens and usage of nuclear weaponry.
And there are many more like companies controlling whole countries, many little factions protecting the world sometimes fighting with each other, etc.
But I liked some of the ideas, and I will twist some of mine. Thanks!
A big part of battle academy are the interpersonal relationships, how well does the MC get along with their friends and teammates, rivalries that are both with people who they get along with and who they don't. Also well made deuteragonists will also make the story better
Not too familiar with the genre but here's my take...
I like it when there's a big cast at the beginning, like a whole lot of folk that go through vigorous tests until only a few prove capable of following the curriculum. This adds a sense of weight to their training and is also a great way for char intros imo.
I'm also thinking about events and tests outside of the academy, with them flying over lakes, going for training in jungles, deserts, icefields etc. See how they face off with mosquito bites and frostbite and the like, how they function as squads(or don't.)
I am happy to find that writing a team rather than a single main character is a good idea, and I am even happier that I chose that route on predesign.