Mew, now an UU? What happened? To quote from the 4th Gen POTW, "Mew, the Pokémon of endless possibilities. ...Needless to say, all of this gave it an immediate ticket to the Uber environment." Now it's at the other end of the spectrum, while Celebi and Victini are still considered OU Tier? Rant aside, Mew is still a good Pokemon. Base 100 stats across the board means no obvious weakness to target (Trick Room against fast Pokemon, Physical attacks against Pokemon with low Defense, etc.) with the possibility to go down any path it wants. And unlike the aforementioned Celebi and Victini, Mew has the movepool to do anything. 5th Gen did nerf Mew of several good attacks, though, but what's left is still more than enough to make a threat.
Now, for my suggested moveset;
-Psyshock/Dark Pulse/Aura Sphere/Giga Drain/Vacuum Wave/Surf/Ice Beam/Thunderbolt/Thunder/Flash Cannon/Energy Ball/Grass Knot/Scald/Charge Beam/Psychic/Solarbeam
Attached Item: Life Orb/Choice Scarf/Expert Belt
EV's and Nature: 128 Attack / 128 Special Attack / 252 Speed
Naive (+ Speed, - Special Defense)
A mixed sweeper set. Hit hard, hit fast. Dragon Claw is your primary Physical attack here; good power, good coverage, no immunities, only stalled by one type. Earthquake gets rid of any Steel types who can't get airborne and comes with good coverage and power on it's own. The automatic super-effective hit on Tyranitar (an otherwise troublesome counter) is just a bonus. Use over Stone Edge on this set. The Fire attack is primarily there to get rid of Skarmory and Bronzong, but the X4 hit on Ferrothorn, as well as hitting Weavile, is also good. (I prefer Flamethrower myself, but Fire Blast can be used too) The next attack is basically filler; all options in this post are Special so that no Physical wall can switch in with only your Fire move to scare them. (Some of these require a transfer from 4th Gen to have. I'm sure you can tell which fit this category)
Psychic/Psyshock both get STAB; one is slightly stronger, one hits Blissey and Chansey harder.
Dark Pulse is my preferred choice here. Stops Ghosts from coming in, has a chance to Flinch, deals with Psychics nicely, and unlike Shadow Ball, hits any Normal-type switch-ins who think you'll be sending a Shadow Ball their way.
Aura Sphere/Vacuum Wave don't provide any key coverage beyond a X4 hit on Tyranitar and Weavile, though that alone may justify using them. Aura Sphere is stronger and can't miss. Vacuum Wave, however, is Mew's only reliable source of Priority. Sucker Punch? Haha, don't ever consider it; there's a reason I called Vacuum Wave Mew's only reliable Priority move.
Ice Beam hits Dragons, Gliscor (who could otherwise wall this set), and has good power. No real downsides besides "4 Movepool Syndrome".
Thunder/Thunderbolt stops Bulky Waters, mostly, but are both good attacks. I recommend Thunderbolt, unless you can ensure constant rain.
Charge Beam is weak, and has Thunder/bolt's coverage. The possible boost to Special Attack is what earns this attack a slot as an option. (don't use with Choice Scarf, as you'll be switching around too much)
Surf/Scald hits Bulky Grounds and gets a nice hit on Tyranitar. One is stronger while the other has the potential to Burn, which will scare off most Pursuit users.
Flash Cannon doesn't get any noteworthy super-effective coverage, but does have the (too frequently overlooked) potential to lower the foe's Special Defense. Granted, only the Fire Attack will benefit directly, but any Special sweepers you send in will love it.
Giga Drain/Grass Knot/Energy Ball/Solarbeam serves to hit Bulky Grounds and Waters in one moveslot. Giga Drain provides healing (and got better this Generation) that Mew can use. Energy Ball is reliable and like Flash Cannon can lower the foe's Special Defense. Grass Knot can be stronger than Energy Ball, but most of the time will be as good as/worse than Energy Ball (see Vaporeon). Solarbeam is only to be used with Sun support; otherwise forget it.
As for items, Life Orb comes with it's overtyped pros & cons; 1.3X more power to your attacks at the cost of 10% HP. Choice Scarf gives Mew a potential 656 Speed, while locking you into a single attack. Expert Belt is the safety option. A flat 1.2X boost to super-effective hits won't impress everyone, but that bonus is almost certain with the above moveset, which relies more on wide coverage to deal damage than raw power.
The EV spread keeps your offenses equal so that opponents can't count on their Gliscor (for example's sake) eating a weak Flamethrower while remaining otherwise untouchable. Max Speed is essentially mandatory; you want to outrun anything that you need to crush, while preventing most threats from outrunning you. You could take some EVs out of Speed and put them into Mew's offenses, if you would like the extra power. If so, try 168 Attack / 168 Special Attack / 174 Speed. Me, I don't recommend it. Naive boosts your Speed without hurting your offenses. You could run Hasty (+ Speed, - Defense) but I say go with Naive: a Burned Pursuit-user may lack the power to OHKO you if you don't run, if you use Naive.
FIGHTING TYPES! Machamp, Breloom, Lucario, Gallade, Terrakion, it doesn't matter who, just run one! Tyranitar, Weavile, Bisharp, Blissey, even if you are running a Fighting type move on this set, you'll want something to ensure that these, and other Psychic-stoppers, pay dearly for your loss. Having a Dark type is also recommended; most Ghosts have little reason to fear the attacks listed here (except for Dark Pulse), but run the second a Dark type hits the field. Weavile, ironically, is a wonderful partner; it can take out most Ghost types with little trouble, and has STAB Ice attacks to use on Gliscor. If you're running Thunder, then Politoed (or Kyogre, if you use this Mew in Ubers) is also recommended. Ninetales (again, Groudon if in Ubers) is mandatory if you run Solarbeam, but still gives your Fire attack a boost. If you're running Choice Scarf, you better pack something to clear entry hazards. Forretress, Espeon, you get the idea. Also recommended, if you have something that runs Work Up and Baton Pass in the same moveset, it will really make this Mew's life easier. (don't use with a Choice Scarfer, though, otherwise the boost will be wasted) In general, most teams already have one or more Pokemon that works well with Mew. In this case, if you have a strong Pokemon who can break walls (or benefits from an opponent's walls being weakened/terminated), run it. Blissey might laugh off a Galvantula (for example), but if it ate a Special Defense-drop from this Mew's Flash Cannon or Energy Ball, it's going to have to either risk taking a STABed Thunder (not likely) or switch (most likely).
Bulky Ghosts tend to be your safest first line of defense. Super effective STAB attacks, the Defenses to withstand un-STABed Physical attacks, you get the idea. If your name is Spiritomb, then you are the best bet to stopping this particular set; STABed Sucker Punch (quite possibly the only time this attack is reliable) will kill this set no matter what your Speed is. Other Ghosts work too, just run Protect in case of Dark Pulse. Bulky Waters and Grounds also work, having a built-in resistance to Earthquake and Flamethrower/Fire Blast and the Defense &/or HP to take some un-STABed Dragon Claws. Just watch out for the possible Grass or Electric attack. In this regard, Gliscor is especially dangerous; if Mew lacks Ice Beam or a Water attack, this Mew can't touch it. Any Dark type that doesn't pack a secondary typing that renders it weak to Earthquake or Flamethrower/Fire Blast is preferred, but not mandatory. Weavile and Bisharp both have their Priority moves, but have to make sure that Earthquake and Flamethrower/Fire Blast are out of the question. Tyranitar is a classic counter, just make sure your Defense is maxed out so you don't lose out to Earthquake. Zoroark may be better than either of these options, though. Being a pure Dark type, all you really have to look out for is the possible Aura Sphere or Vacuum Wave.
All these counters assume you are not running a Choice Scarf on this Mew. If this Mew is running a Choice Scarf, then you can add some options. Pursuit is almost a foregone conclusion in this case, unless you switched into a Scald and got a Burn before you could attack. Chandelure with Shadow Tag gets a special mention; if you switch into any attack other than Earthquake or Dark Pulse (or any possible Water attack), you can boost to your heart's content then finish Mew off with one blow. Dugtrio needs to watch out for the possible Grass or Water move, but if Mew lacks it, Dugtrio can switch in as Mew attacks, then finish it off with Sucker Punch the next turn (give Dugtrio a Focus Sash, just in case you get hit with a STABBED Psychic/Psyshock). Oh, and field hazards; keep at least a layer of Stealth Rocks up, and a few layers of Spikes & Poison Spikes too. Mew may not be weak to these, but constantly switching in and out will lead to a self-inflicted KO if not careful, and can't Synchronize off the Poison from the Poison Spikes.
A final word about this moveset's counters; almost all of them CAN find themselves KO'd depending on what is in Mew's final moveslot. A scout with Protect is highly recommended so that you don't send in something like Gyarados only to learn the hard way that Mew's carrying Thunder/bolt. (that was just an example, but you get the idea)
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I don't calculate stat values, I don't use cheating devices, I don't breed my way to perfection, and I don't care about natures. I catch my Pokemon the way they are, and treat them like individuals instead of brainless drones. If you use this philosophy, copy & paste this into your signature. (Started by Tyranitar, "I don't use "uber" Pokemon," edited out by me because I do use "uber" Pokemon on occasion.)