How To Get Mewtwo in Pokémon FireRed/LeafGreen Version
Note: You must obtain HM 03 Surf to reach Mewtwo's platform.
To unlock Cerulean Cave, you must beat the Champion, catch 60 Pokémon, obtain the Rainbow-Pass from Celio, collect the Ruby and Sapphire on the Sevii Islands, and lastly give them to Celio for that guy to leave the Cave's entrance.