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Rather than something like the King of the Pirates or becoming the Hokage, I'm pretty sure the reason they never defined the term is so that kids can interpret it any way they want when they watch the anime or play the games
For some, it's catching em all
For some, it's the hall of fame
For some, it's beating all their friends
For some, it's the World Championships
For some, it's assembling the strongest team
Rather than a goal with a set end point, this allows the audience their own interpretation for what to be invested into,
"I wanna be the very best, like no one ever was" can mean whatever you believe it should