Perseus Jackson-Wayne is sick. That's a fact that trailed behind him his entire life. Bruce had a ton of muscle, Dick was a gymnast, Jason had a lot of his own strengths and Perseus was the sickly, weak Wayne.
His nose bled at random. His joints hurt and swelled. At times he couldn't breathe, plagued by asthma. His immune system was dead.
He thought this would be his forever, exceptions from gym class and regular doctor visits.
Boarding schools make it a bit better, but so often is he still in large, polluted cities, he's still ill.
He's a demigod. The Minotaur is chasing him, and it's raining, and how is he running so fast, so long? He kills it and passes out.
When he wakes up, he almost gets whiplash. For the first time in his life, Perseus Jackson-Wayne Percy Jackson feels healthy. He doesn't feel completely pain-free, but he just fought the Minotaur, that's to be expected.
But the air and water here are so clean, he feels like he can actually breathe.
Percy Jackson is the son of Poseidon, the sea, and the waters in Gotham are screaming, dying, no longer water.
Later, after a few years, he'll learn just coming to Camp doesn't immediately fix things. It still takes a few days to get the poison out of his system, but it's such a big difference regardless.
He considers staying year round. He could be okay. He could leave the illness. But in all worlds, Percy Jackson is loyalty, and he won't leave his family.
So, year after year, Perseus Jackson-Wayne returns to a city that's killing him. Year after year, he gets worse.
(And imagine this is one of those au's where Percy is a prophet or otherwise entangled with Apollo. Imagine, the God of Medicine feeling his menteé slowly killing himself. )