Instructions
Beat the Elite Four after collecting all eight Gym Badges. The entrance to Cerulean Cave will now be unblocked.
Follow the maze to the bottom level of the cave. Mewtwo will be standing at the end of the pathway. Save before you engage Mewtwo in battle.
Use the Master Ball on Mewtwo if you have saved it. As difficult as Mewtwo can be to catch in a normal PokeBall, a Master Ball has a 100 percent capture rate.
Attack Mewtwo with moves that will impair its abilities, such as Hypnosis or Shock Wave. Putting Mewtwo to sleep or paralyzing it will increase your chances of catching it in a lesser PokeBall.
Bring along Pokemon that know Bug-, Ghost- and Dark-type attacks because they are very effective against the psychic Mewtwo. Forretress, Shedinja and Carvanha are all excellent choices to whittle away at Mewtwo's health because of their natural Bug, Ghost and Dark abilities.