MOO2

For all intents and purposes, Mewtwos are just as combat capable as any other Legendary, possessing powerful Auras and designed for killing.  That said, they ain't perfect.

1. You discover that Mewtwos, generally, are not kept in Pokeballs.  If they are, it's always a Master Ball and even then records indicate it's a rather uncertain process.  This leads most experts on the subject to come to two conclusions:

A) Mewtwos might be Pokemon, but they are much less volatile in form than other Pokemon are.
B) This is likely due to their human side.  Like you can't store a human in a ball, doing so to something that's half-human must be extremely painful and difficult.

Catching them is certainly out of the question, but if you could get your hands on a Masterball, or maybe even one of these half breed balls, you and Chione might be able to SCIENCE up a weapon that acts like a sickening laser that is sometimes used to calm down crowds.

2. Mewtwos will do almost everything in their power to protect their symbiont.  Much like genetic twins sometimes develop a pscionic connection, a Mewtwo does to its symbiont as well.  At any time their human side is at risk, they will immediately drop anything they are doing to assist.  This can get hazy and hasn't been tested much in terms of how far they'll go to harm themselves either, i.e., 'Kill yourself or the little kid dies.' isn't really something that's come up with this.

On this note, far as you can tell there's no reason a symbiont -has- to be a child.  It certainly would have to be human, given there is a genetic link between the symbiont and a Mewtwo.  What seems to be the issue with an adult taking this place is the Mewtwo doesn't mature as well.  Children are very creative, learn fast, and are naive and impressionable, not to mention possess have actively growing brains.  This helps facilitate the growth of a Mewtwo as well.  You don't really...bring up much on the downsides of an adult symbiont, because while there's proof it's been tested and done, the results seem to be absent.

3.  As a hybrid being, their genetic structure -is- quite exploitable.  Seems they are capable of coming down with most illnesses that effect either Pokemon or humans, and those that effect both can have quite nasty symptoms.  A popular counter measure in earlier decades was a specially engineered strain of Anthrax that targets a pscionic's brain, causing a very powerful reaction that is fatal to most mortals.  These things, being part Legendary, aren't straight out killed by it, but it severely weakens them and is probably the most painful thing someone can do to them.

Radiation based counter measures against Mewtwos aren't super popular for many reasons, but far as you can tell there's nothing genetically that would stop this from working, especially if these things don't have full on Mew D.N.A.  That said, there's very little research on Dittos from this sorta standpoint.  Most you can find on counteracting them is they got a lot of immunities to these sorta things, and don't bleed.

4. Development of Mewtwos relies heavily on Dreamworld tech and using dreams to accelerate mental development.  It makes these creatures very susceptible to dream smoke.  If exposed to it in a raw form, they tend to enter a share 'day dream' with those in the immediate facility.

5. There is a problem here, though.  The Mewtwos in question are machine augmented.  You can't say for certain what sort of things this might do to shield them.  After all, one has to wonder why she augmented them.   That said, it might be another thing you could target.  Their augments are probably military grade, but if you could find a way to disable them or damage them, it would probably do a good bit to limit their combat potential.

6.  There is one very particular stimulus that all Mewtwos on record have reacted to the same way (assuming it was presented to them).  Encountering a Mew is a very shell shocking experience to them.  Research documents it like meeting their mother for the first time.  They become meek, calmed, wishing to learn about the creature and win its affection.  If their symbiont acts in a way to try to prevent this, it causes them to experience pretty severe emotions.

Granted, you don't know where the hell you can find a Mew, but some folks you do might have a clue.