My Mewtwo's moveset in Fire Red:
FLAMETHROWER 21 PP
Works great for Ice and Steel types (Steel resists so many types). Strong move with burning possibility and high PP and I have made it even higher.
ICE BEAM 10 PP
For Flying, Ground and Dragon types but also for rival's Tyranitar because it resists all the other moves.
SHADOW BALL 15 PP
Basically for Psychic and Ghost types but also a good non-Special Attack move for good Special Defenders.
PSYCHIC 16 PP
Of course. Mewtwo's Psychic. Try to name more iconic duo. This STAB move exterminates everything so I had to boost its PP to the max just like Flamethrower's.
With these moves you dominate the Pokémon world and easily humiliate elite four (even the 2nd round) by destroying every single Pokémon by one hit (except for Tyranitar which needs two Ice Beams).
With my 100 level Mewtwo with this moves I can easily level up weaker Pokémon with Exp. Share and just walk over the opponents to the Hall of Fame as many times as I want. It doesn't require any healing items.