Swords Dance: the first move that came in mind when I thought of Petrel was Swords Dance, though... given his lore, he probably wouldn't use it very often - if at all. it primarily serves him as a reminder of his past more than anything else, and as much as he wants to get rid of it, it's just... there. sort of like an HM, but not really. maybe he has the lingering feeling that he needs to use it just in case harm comes to him or his loved ones, but other than that, it's honestly more of a burden on him than a move he'd be comfortable using.
Focus Energy: Petrel is the type of character who's extremely determined/dogged when the situation calls for it, and I think this move captures it nicely! in the game, it increases the likelihood of a critical hit; however, but for Petrel, it steels him for whatever he needs to do. this is one of the moves that he learned after moving to Isei's village, and although he probably wouldn't use it much (considering that he's already a pretty focused character), he'd rather have it than the move it replaced.
Wing Attack: Petrel likely had a more attack-based moveset while working for his cult, but after leaving it, he most likely did a 180 and decided to adopt a status-based moveset instead - forgetting his attacking moves in favor of something more "peaceful" (so that he could turn over a new leaf potentially). Wing Attack is an exception to this, not only because it's a reference to his name (haha bird reference funny), but also just the fact that an attacking move would be useful in cases of self-defense and the like. he likely had a stronger Flying-type move beforehand (like Fly or Brave Bird), but Petrel now likely thinks that this move is a nice balance between "capable" and "not totally destroying the opponent in one hit."
Rest: it's mentioned in Petrel's bio that he can fall asleep anywhere, so... *jazz hands* Rest ends up taking his last slot. he'd use this move probably... every so often? which isn't too frequently at all, but it's probably the one that he'd use the most out of all the ones I listed lmao. the move itself can be used in a variety of situations, which Petrel would probably appreciate. as with Focus Energy, he learned it after running off with Isei, and although it's sort of redundant at times, he'd rather have this move than whatever he had previously.
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- oh.... heck yea.... Aromatherapy is an especially interesting move as it seems like an allusion to her origins as a resident of Floaroma Town haha. but yea, Dolores being status-oriented makes a lot of sense... she'd likely just exist to help her teammates and would therefore be pretty useless in a single battle lmfao.