The Cerulean Cave is filled with the strongest wild Pokémon. It's quite an interesting place to navigate, because it feels like you'll never reach where you want to go. After going through mazes several times, you'll find Mewtwo between two rocks.
Capturing Mewtwo
Mewtwo is a lv. 70 Psychic Pokémon; the strongest Pokémon in the game. Do not use the Master Ball, and hopefully, that wasn't used already. Mewtwo is nearly impossible to catch, but that doesn't mean he is impossible. Try to paralyze him with Pikachu or a fast Dragonite/Dragonair, then weaken him down to red health. Then throw Ultra or Great Balls. After a lot turns have past, start using the timer balls. After catching Mewtwo, you should be proud to be the owner of the most powerful Pokémon in the original 151!