Like the rest of the Legendary Pokemon found within the game, Mewtwo is an extremely strong Pokemon that will be both difficult to defeat in battle and capture afterwards. However, there are a number of things players can do in order to make Catching Mewtwo easy to do. First, Steel Type Pokemon work well against Mewtwo when in the battle portion of your first encounter with it, since they don't take much damage from its attacking moves of Psychic and Swift. Slowly killing Mewtwo to death with Toxic is also a smart strategy, as Mewtwo will eventually go down no matter how many times it uses Recover. (Just make sure not to run out of time in the battle portion if you do go with the Toxic Method.)
Once Mewtwo has been defeated and the capturing portion of your encounter with it begins, it is highly recommended to use the Master Ball you obtained after defeating Team Rocket at the Silph Co. The Master Ball will automatically capture Mewtwo if you hit it with it, being the simplest of ways to nab the Legendary Pokemon. However, if you don't have the Master Ball or don't want to use it on Mewtwo for some reason, then make sure to use Razz Berries, Silver Razz Berries and Golden Razz Berries on it while throwing nothing but Ultra Balls. Razz Berries make capturing Pokemon far easier to do, and Ultra Balls have the highest catch rate within the game outside of the extremely rare Master Ball. (Make sure to watch out for the barrier Mewtwo will randomly put up, as it prevent the use of Berries and Poke Balls against it.)
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