No but you can rent a Mew. Complete all the Stadium modes, the Gym Leader Castle, and beat Mewtwo in the VS Mewtwo mode and you will be able to select Mew as a rental pokemon in the Prime Cup mode.
If I were you I would uses very powerful pokemon.
beat the Pokemon league and beat N and you use your Master Ball to catch him
if you beat the boss of team galactic, you will get a master ball from him
when you beat Dialga you get the Master ball NO! It's when you beat Cyrus of Team Galactic the first time!
it depends what one you want but just beat all thegyms and you will get some
After you beat the elite four.
beat Cyrus in the veilstone base
Cyrus gives it to you when you beat him.
try to use a giglarchan or maybe a tigra it would help
your rivel or in ruby its may. after you beat the Pokemon leag its YOU . . ( .) ( .) O O
you have to beat team rocket in silph co and beat giovani.