Background Information!
Mewtwo the
Genetic Pokemon! Mewtwo is a very iconic Pokemon even recognized among many first timers to the franchise. Originally created to be the most powerful Pokemon in existence and for many times, he even surpassed that of Arceus's stats thanks to the power of not one but two mega evolutions. Created by a team of scientists headed by the mysterious Dr. Fuji, Mewtwo was intended to be the most powerful Pokemon in existence. His most iconic role is undoubtedly Mewtwo Strikes Back, the very first Pokemon movie that depicts Mewtwo's identity crisis of where he belongs in this world. I personally recommend you watch the Japanese version. However his most iconic role as Mega Mewtwo X and Mega Mewtwo Y is undoubtedly Pokemon Adventures XY Chapter where we see
the Monster of Cerulean City mega evolve and take on one of the most dangerous foes of the Pokemon series. However Mewtwo's most memorable role in Pokemon Adventures is also undoubtedly one of the greatest Pokemon battles in Pokemon history, Mewtwo the Genetic Pokemon vs Deoxys the DNA Pokemon, both Pokemon whom share categorizations that are the exact same but these two Pokemon couldn't be anymore different. Well, enough about that.
Mewtwo Unbound (Special Sweeper)
Mewtwo
Item: Mewtwonite Y
Ability: Unerve
Nature: Timid (+Spe/-Atk)
EVs: 252 Spe/252 Sp. Atk
Psystrike/Psychic
Ice Beam/Dragon Pulse
Flamethrower
Focus Blast/Aura Sphere/Calm Mind/Energy Ball
Nough said but Special Mewtwo is an obvious set. With it's ridiculously high 140 speed, it can literally out speed most Uber-class Pokemon easily. Combined with it's Psychic STAB and it's 4x coverage against many dragon and steel types that have 4x weakness due to their type combinations, Mega Mewtwo Y sweeping potential is simply amazing. In fact Mega Mewtwo Y pretty much has everything it needs to sweep almost every Pokemon to the point that it's 4th slot feels more like an extra add-on that you can essentially just put any extra move you feel you need. The only real necessity the 4th move slot has is to counter Pokemon such as Darkrai or Dialga who are one of the few most dangerous counters to Mewtwo.
Monster of Cerulean City (Physical Sweeper)
Mewtwo
Item: Mewtwonite X
Ability: Pressure
Nature: Jolly (+Spe/-Sp. Atk)
EVs: 252 Spe/252 Atk
Zen Headbutt/Earthquake
Low Kick/ Drain Punch
Ice Punch
Bulk Up/Taunt/Rock Slide/Poison Jab
Mewtwo's most famous title outside of it's categorizations is the
Monster of Cerulean City due to Mewtwo's fearsome strength that cause awe-struck fear to the nearby inhabitants of Cerulean City during his stay at Cerulean Cave. His fearsome strength just got better with Mega Mewtwo X! Mega Mewtwo X is so feared by competitive players that you don't even need Zen Headbutt, Mewtwo's best physical Psychic STAB move, among your four move-slots if your considering only type-coverage. Zen Headbutt is powerful thanks to STAB but many people also consider using Earthquake as it covers a wide variety of threats more than Zen Headbutt does. Low Kick is obvious as it's great against heavy Pokemon, especially Rock or Steel Types. Drain Punch is an alternative to both Low Kick and Recover if your looking for an effective fighting-type move but also recovery power. Ice Punch is obvious against dragon types and similar to Mega Mewtwo Y, the fourth slot feels somewhat like an extra but important layer of coverage then a central role to Mewtwo's set. Bulk Up is obvious to increase sweeping and defensive power. Rock Slide is to counter against the dreaded Ho-Oh and by extension other powerful flying-types, like Zapdos. Poison Jab is meant to be a counter against Fairy-types as Mega Mewtwo X has gained both a new strength and new weaknesses thanks to his additional fighting-type.
Mewtwo Strikes Back Double Set (Huy's VGC Tank Mewtwo)
Mewtwo
Item: Iron Ball
Ability: Pressure
Nature: Sassy (Sp. Def/Spe)
EVs: 252 HP/252 Sp. Atk
Trick Room/ Psychic (Depending on who's the Trick Room user)
Explosion/Aura Sphere/ Focus Blast
Protect
Blizzard
This is partially based on Huy's VGC Mewtwo set. I couldn't find the EV spread or nature so it's just guesses from here on out. The original set is Trick Room, Explosion, Protect and Blizzard which was absolutely devastating to unsuspecting players thanks to Mewtwo's Bulk and outspeeding others under trick room. In a meta still dominated by fast heavy-hitters, tanky Mewtwo will genuinely be a surprise taking down many Uber Pokemon who hae an ice-weakness. Other alternatives are also Aura Sphere and Focus Blast to deal with the heavy usage of dark and steel-types in upper metas and if you plan on using a different trick room user, Psychic is a good replacement too.