You have to unlock Mewtwo first.
I could unlock Mewtwo in my sleep. In fact, I did.
EDIT:
Jigglypuff Complete Classic or Adventure Mode or play 50 vs. battles.
Dr. Mario Complete Classic or Adventure Mode with Mario without continuing or play 100 vs. battles.
Pichu Complete Event Match #37 : Legendary Pokémon, or play 200 vs. battles.
Falco Lombardi Clear 100-Man Melee or play 300 vs. battles.
Marth Play Classic Mode with all fourteen regular characters, or use them in VS. mode or play 400 vs. battles.
Young Link Complete Classic Mode with ten different characters (including Zelda and Link) or play 500 vs. battles
Ganondorf Complete Event Match #29 : Triforce Gathering, or play 600 vs. battles.
Mewtwo Play VS. mode for a combined total of twenty hours or play 700 vs. battles.
Luigi Complete Stage #1 of Adventure Mode with the time ending in a "2" in the second's slot, then beat Luigi and Peach in less than a minute or play 800 vs. battles.
Roy Complete Classic or Adventure Mode with Marth and without continuing or play 900 vs. battles.
Mr. Game & Watch Complete Adventure, Classic Mode, or Target Test with all other characters or play 1000 vs. battles.