Pokémon FireRed and LeafGreen/Cerulean Cave

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 between two rocks.

Capturing Mewtwo
Mewtwo is a level 70 Psychic Pokémon; the strongest Pokémon in the game. This Mewtwo knows the moves Psychic, Swift, Recover, and Safeguard. Do not use the Master Ball (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 before he uses Safeguard, then weaken him down to red health. Mewtwo will Recover when its weakened. When you finally manage to get Mewtwo's health down to red, 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!