Percy goes to Gotham University because plot reason and he has an accident where he's taken to the hospital and his blood is tested, and it pings something in the Batcave, not because of the weird godly biology, but because this random ex child terrorist, Perseus Jackson, is somehow Damian's biological half brother? Well, you see, Sally and Talia used to date and Poseidon as there too, and magic is a thing, so Percy has three biological parents. Best thing? Damian totally knows about his half brother and loves him. Perseus al Ghul-Jackson is his menace of big brother that taught him that he doesn't need to be perfect because if Percy can fire a cannon against a school bus and dump his entire class in a shark thank and have Ra's and Talia laughing about it at dinner, Damian doesn't need to be afraid of having some mishaps [that boy had too much pressure on his shoulders].
Bruce is losing his mind about this random al Ghul coming out of nowhere and making countless contingency plans for him [for the wrong reason, mind you] only to find out that Percy isn't a secret at all! Damian's talks about him all the time. He is the guy that taught him how to sword fight, that taught him how to swim, how to bake cookies [Blue Cookies!!], and Ancient Greek of all things! Percy is all of Damian's stories about his time living with his mother and grandfather and they all just thought he was some kind of instructor or over achieved babysit or even an imaginary friend considering all the absurd things Damian had said he does [he sassed Ra's and lived to tell the tale!], but no! Percy is real, and his brother! Percy is his coolest older brother [Dick is crying in the corner] that happens to visit him at the League as if it was a resort vacation [compared with the rest of his life, it was] from time to time when he wasn't battling gods [Bruce doesn't have this information yet] that both Talia and Ra's really loves [he is their boi] and did his best to mak sure Damian had a normal-ish childhood since he knows that some adults can forget about how it's important for the kid to be normal-ish even if they're demigods or part of cult of shadows and furry vigilantes.
Not only that, but Bruce entertains committing himself when he realises that Percy has a great relationship with Talia and Ra's [no bashing here!] and that the al Ghul's are his healthiest family members [no one can beat Zeus' bullshit and Hera's whole thing]. The little shit Bruce has yet to lose jumps of the window when Percy shows up to a family dinner and Alfred and him are besties [Alfred is a legacy!].
Then, we have Bruce losing his marbles trying to understand this weird al Ghul that doesn't act like an al Ghul and has a bigger rep sheet then post-Pit Jason but is just a chill New Yorker surfer [some how]. Dick is having a identity crisis because he isn't Damian's coolest older brother anymore [suck it, Ric Boy]. Tim has a murder board about him [and Bernard is on the background laughing because he is a son of Dionysus and he knows all about Percy and his Buzzfeed unsolved], and Jason is like “oh yeah, I knew about him, we used to hang out at the League”. Duke and Cass are the only normals about the whole thing, and Steph and Babs are there for the Keeping Up With the Waynes drama of the week.
And all this drama is before we add the others to the equation. Like, once we have Annabeth Chase [run away from at seven only to show up five years later], Thalia and Jason Grace [both supposedly dead], Nico di Angelo [Victorian, Italian boy that doesn't legal exist], Grover Underwood [five years in the fifth grade!], Hazel Levazque [yet another legally dead/doesn't exist situation], Leo Valdez [known arsonist], Frank Zhang [didn't he burned his grandmother's house?], Piper McLean [what is she's doing here?] and Rachel Elizabeth Dare [what the hell?], they will all need a big murder board and more red strings.
The Batfam is working with the idea that Percy is collecting Buzzfeed Unsolved's kids like Pokémons [they also think he has his own cult outside Ra's'].
