Pokemon Legends: Mewtwo. You play as kid in modern-day Kanto with psychic powers, which are ... kind of okay against wild pokemon, but not to the extent that they can just replace any part of the standard Legends gameplay loop (and you're forbidden from using them in battles against other trainers, meaning you still need to have a team of pokemon); also the type-matchups are still a thing, so i.e. it's less effective against Steel and Psychic pokemon, and ineffective against Dark pokemon. Maybe some kind of penalty for not using mostly Psychic pokemon? Because, like, you're "a psychic trainer", that's your trainer-class, you're supposed to use Psychic-types. ... hm, maybe your powers are a bonus for catching and raising pokemon, but only for Psychic-types, and the rest they're just for combat-only.
Mewtwo shows up because it thinks your abilities are "interesting", and it spends the game with sort of ambiguously a mastermind-and-pawn kind of thing going on with you; your dynamic with Mewtwo is always just a little bit antagonistic, though this is partly because Mewtwo is Vegeta-tsun about being friends with you. Mewtwo is a frequent ally, but you can't give it direct commands in battle or do anything that counts as actually capturing it for most of the game, and in fact Mewtwo is functionally your Rival as much as anything else. It tries to keep out of sight when there's other humans around, but the protagonist nevertheless develops a Reputation, both due to the fact that an artificial Legendary Pokemon frequently hangs out with them, and the way the gameplay obliges you to use your powers.
The main plot basically has you caught in the middle of a three-way fight between Mewtwo's original creators, a second faction who comprises the main villains of the game, and Mewtwo itself. After all that's resolved, the final boss has you on the post-volcanic ruins of Cinnabar Island going one-on-one with Mewtwo, with just your powers, framed as the culmination of your rivalry, your friendship, and of you finally throwing off Mewtwo's authority over you. As the fight progresses, you and Mewtwo just sort of start floating off the ground, and before you're halfway through, the two of you are just flying around above the island. The music is a sort of Endwalker: Footfalls arrange of the Mewtwo battle theme from Pokemon X&Y; this is also the game's main themesong. After you win, Mewtwo formally joins your team, but doesn't use a pokeball, and instead just follows you around openly. None of this helps your reputation.
After you capture every other pokemon, the True Final Boss in the postgame is Mew.