Wow, really?
ARE YOU SERIOUSLY CHANGING MEWTWO AND BOWSER? MEWTWO CAN'T WIN! TMS OR NO TMS, HE ISN'T GOING TO WIN!
Aura Sphere is range-limited, as seen when it misses Fly. Bowser can teleport out of range, wait for Embargo to wear off, and then invincify himself.
I did prove at some point how Mewtwo could win. >_> And I wasn't using aura sphere anyway.
Future sight hits trough any means of protect, fly, dig... only sp.attack and sp.def are applied. teleport is also veery slow to move and has shadow easy to follow. Mewtwo can also levitate.
Embargo disables the use of Star rod and other items.
Substitute makes mewtwo safe from status ailments, also takes any attack for mewtwo
Recover to recover health
And basically the match goes like this:
Mewtwo as the psychic pokemon, according to PMD, has telepathical powers (see the video I posted) and psychics in pokemon world are usually equipped with premonition powers as well. While Mewtwo talks normally on PMD, he shows he's able to enter the minds of the pokemons that wandered to his cave, thus mind reading is not out of the question but actually very plausible scenario.
These are not neccesarily needed however, as Bowser's taking out the Star Rod and activating it takes more time than Mewtwo being able to initiate Embargo and disable Bowser's Star rod plus other items. While if Bowser instead opts to wait out and try and use his status ailment move, substitute is quick enough to be pulled off. Or we could even switch this out with Protect as it's a priority move, thus being able to block out any status ailment or even physical move once in a while from Bowser if he so tries, or Safeguard.
However, if Bowser uses his stoning move (lol) and Mewtwo pulls off his move to counter it, Bowser takes 8 seconds to whip out his Star Rod at minimum, plenty of time for Mewtwo to utilize his most powerful psychic abilities in the pokemon verse and his speed to embargo Bowser, leaving him unable to utilize it. On realistic scenario, Bowser would be cocky and dumbfounded when his moves didn't work, thus allowing even more time for Mewtwo to do his moves. Mewtwo is made to fight and engineered as such.
For Mewtwo's moves then, he can use Future sight which hits trough any means of protect, fly, dig and even shadow force using Giratina and ignores weakness, resistance and things. Only Mewtwo's awesome sp.attack and Bowsers special defence (which is lower than his defence) are taken into account. Future sight has 90% accuracy, so it's hard to miss. In the meantime Mewtwo can dodge Bowser's other means of attacks if he does anything besides teleport, pressures bowser, heals himself, embargos some more and protects himself via substitute/protect.
Also, if Bowser lacks any kind of anti-status ailment move, it would be possible for mewtwo to use toxic on him before he uses his star rod (unless ofc invincibility removes status ailments).