Use lots of Ultra Balls and hope for the best! Use moves such as Thunder Wave or Hypnosis to increase your chances as well. Keep re-encountering the Beast in the manner previously outlined and chip away at its health until red.
You can expect Mewtwo to know the moves Psychic, Swift, Recover, and Safeguard. Mewtwo is a level 70 Psychic Pokémon and considered to be the strongest Pokémon in FireRed/LeafGreen. Surf your way directly to your final destination! Head west and then walk through the ledges towards the small lake. If you have been following the previous instructions you should have exited back to the 1st Floor, with one ladder directly north from you, and accessing it should have led you here.
Feel free to battle the powerful Pokemon here and pick up the items, but if you want to reach Mewtwo as soon as possible, you must reach the stairs at the middle of the map to access the right route.