i think that when mewtwo gets to level 100 it should have these moves.
shadow ball,pychic,aura sphere,and recover
that's all the information i have and don't get the national pokedex if you do you have to get a mew from someone who has Pokemon emerald and has won the old sea chart in a Nintendo contest to get mew.
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Mewtwo is the ultimate Psychic type legendary Pokemon. It was introduced in the first generation and does not evolve into any other Pokemon, although as of the sixth generation it can mega evolve into Mega Mewtwo X or Mega Mewtwo Y.
It really depends upon how much they are trained and which moves they know. Mewtwo is stronger but Mew is more skilled. Presumably, if Mewtwo calmed down a bit and trained more, Mewtwo would have the advantage.
ice beam psychic aura sphere recover
In Pokemon Diamond and Pearl Mewtwo learns the move Aura Sphere. However, in the other games Mewtwo learns all it's moves before it reaches level 100.
It can learn Future Sight, Shadow Ball, Thunderbolt, Thunder, Flamethrower, Fire blast, Earthquake and many more moves.