Okay so season 1 was definitely Percy's story like between the flashbacks and his development over the quest The Lightning Thief is Percy's Story. The whole series is Percy's story but the way they produced the first season of the show is especially Percy's, and I need them to continue to develop this in the rest of the seasons.
Season 2, Sea of Monsters, should definitely be Annabeth's. Percy (and the readers) get to know her better--she opens up to him about her past, not just introducing him to the world they share (the Olympians) but to Her World and How it Got to Be that Way. We see more of how who Percy is impacts her (esp with Tyson), and she takes on a lot of responsibility for saving their quest. Unlike the Arch or Crusty, Annabeth is the one that saves them from Circe and takes on Polyphemus one on one.
Season 3 I think is Thalia's. It's the only chance we really have, as readers, to get to know her--we're thrown into her relationship with Percy at the beginning of the book, after our only introduction to her being her saying her name at the end of som, but we travel with her on this quest, and I think flashbacks, etc. in this season should be about her. It's the best way to let the audience get to know her, and I think we need to get to know her to understand her choice at the end (and to be excited when we see her again later). We need that her sudden disappearance at the end, when she leaves without saying goodbye and just as suddenly as she appeared she's gone, to hurt and to feel wrong and making her the Character is the way to do that imo.
Botl in season 4 I think is tricky at first glance (esp since we've given Annabeth som already) but tbh it needs to be Grover's. Flashbacks can be about his time in schools as a protector, and his time searching for Pan. Grover's development is kind of sudden in this story, but I think showing him when he's younger and like as he's been off Doing Things it would be more dramatic and honestly Grover is a fantastic character that Rick seems to forget about/ignore a lot and he should make it up by showing us what his life is like when he's not with Percy (which is increasingly often) and letting us see his independence develop to the point that he's ready to take on his new mantle and be a leader.
Season 5 is obviously Luke's. Even the book is written like that. We need flashbacks to his life and childhood just as much as Percy does, and they need to humanize him and let us empathize with who he was and how he got to who he is by the end of the story before he dies. I think they should give us flashbacks to his quest here, too, and probably the conversation he clearly has with Hermes before he goes on it (he's obviously bitter when he talks about it in tlt, and he had to get his magic shoes, and I think they need to utilize having that conversation in person so we can see how Hermes tries and fails to relate to him and also to make LMM make very very sad eyes as Luke leaves because he knows his son is at the end of his time as a hero). They can milk this for all the comparisons between Luke and Percy. I think flashbacks to his claiming, and not having to move cabins but probably like getting a bed or something now that he's here Forever, and when he becomes the Cabin Counselor. How/when he meets up with Thalia. Him seeking out fights as they make their way to camp. The battles he fights on his quest, facing monsters he's working with now, getting the scar.