If I were paid for all of Mew's movesets, I wouldn't be able to spend it all in a hundred lifetimes. Mew learns every single TM in all of Pokémon, and thus, its versatility is what all Pokémon wish they could have. Except Smeargle, that is.
However, Mew can't really come in on anything without taking a decent chunk out of its health. It wishes it had more resistances to things other than Psychic- and Fighting-type attacks. In the sweeping department, Mew is also outclassed by Mewtwo, who is faster and more powerful. Still, it's Mew's versatility that makes it stand out, so its advantages over other Ubers should be exploited. Mew also has the ability to Baton Pass whatever boosts you see fit, which is truly an extraordinary ability, one that should never be overlooked.
Mew is far and away the best Baton Passer in the game. It learns every TM in the game, allowing it to pass any type of boost it wants. By using a combination of Rock Polish and either Swords Dance or Nasty Plot, Mew can easily and quickly prepare any offensive Pokémon for an extremely deadly sweep. After a few turns with Mew preparing on the field, you can watch your opponent’s team crumble under the sweeper you have turned into an offensive juggernaut. Bring Mew in on a double KO, or into something that cannot do too much damage to it, like Forretress, or something that it can Taunt, such as Wobbuffet, and use Rock Polish while they switch out. When the new counter comes in, you can either boost either Attack or Special Attack if you can live through an attack, or just Baton Pass off if you are killing range, as +2 Speed is much better than nothing.Team Options & Additional Comments >>>
Mew is blessed with a phenomenal support movepool that allows it to fulfill almost any role in a team. With the moves, item, nature, and EVs shown, Mew becomes an amazing lead who matches up well against many common Uber leads and will reliably put you in a favorable position within the first few turns of battle, if it is used properly.
The premise behind Lead Mew is fairly simple: Taunt is for preventing other leads from laying down entry hazards, Stealth Rock is for setting up your own entry hazards, and Explosion is for going out with a bang while hopefully taking the opponent's Pokemon with you. U-turn rounds out the moveset nicely, allowing Mew to switch out of Deoxys-S who Taunt first turn, as well as breaking Focus Sashes and generally being an excellent momentum tactic. However, this set's usefulness doesn't stop there; since Mew can often find opportunities later in the battle to come in and Explode on a threatening sweeper or an annoying wall, it is often in your best interest to keep it healthy for as long as possible. A strategically-timed Explosion can make the difference between winning and losing a battle, so one of the most important things about using Lead Mew is knowing when to sacrifice it and when to save it for later.Team Options & Additional Comments >>>
Mew, along with Smeargle and Ditto, is one of the few Pokémon in the game who has access to Transform. Need a physical wall? Mew can Transform into Groudon. Need a special sweeper? Mew can morph into a Darkrai. The only requirement that Mew has in order to Transform, is that the Pokémon in question is on your opponent’s team. This set’s ability to do well is rooted in its unpredictability. Furthermore, by having Mew Transform into a sweeper who is on or is like one who is on your team, it can take advantage of the damage the other sweeper has already done. For example, Dragon Dance Rayquaza is an incredibly potent sweeper who is only checked by very bulky Lugia and Groudon after Choice Scarf users are dispatched. It also does extreme damage to its checks before it is taken out, to the point where they cannot do their job again. If you have Mew morph into a Pokémon who can take advantage of a weakened Groudon or Lugia, such as Swords Dance or SubSalac Garchomp, it will be easy for you to sweep.Team Options & Additional Comments >>>
Since Mew has access to every TM in the game, it can make good use of this ability by using a set which specializes in crippling your opponent. Your first moveslot is home to a status move which will destroy any chance of your opponent sweeping. Thunder Wave is more reliable, and can be used on any number of opponents. On the other hand, Hypnosis can completely incapacitate your opponent, but it can only be used on one Pokémon, and only has a 60% chance of hitting. In the second moveslot, Mew has the choice of Will-O-Wisp or Toxic, both of which are “wearing” status moves. Will-O-Wisp has the handy side effect of cutting your opponent’s Attack, while Toxic’s damage will grow over time, forcing your opponent to switch out soon or die. Feel free to mix and match, however. You do not have to have one “wearing” status and one “crippling” status.Team Options & Additional Comments >>>
Mew has so many other options it's not even funny. Don't bother with Choice Specs, as Mewtwo is superior in every way. Flamethrower, Fire Blast and Overheat will take care of Scizor, Metagross and Forretress. Shadow Ball can replace Dark Pulse if you prefer the chance of a Special Defense drop, to the potential of flinching an enemy. Stone Edge is Mew's most powerful physical attack against Lugia, and obviously it will destroy Ho-Oh. Silver Wind has low Base Power and PP, making it rather unappealing, but the chance to Baton Pass +1 in every stat, makes it a viable, but not recommended option. Knock Off is a possibility on the Double Status set as an attacking option that also semi-cripples your opponent, however, burning or paralyzing the opponent's Pokémon is generally more useful.
Bulk Up, Barrier, Calm Mind, and Amnesia are all available for Baton Pass sets. Softboiled can also be used on some Baton Pass sets, as it allows Mew to possibly pull off more than one pass. However, it comes at the price of being able to only pass one type of stat boost, unless you go without Taunt.
When using Baton Pass, you may find it better to use either Swords Dance or Nasty Plot with the necessary attacks (and Baton Pass). If you are using Swords Dance, you should use Ice Punch, Earthquake, and/or Brick Break, and if you are using Nasty Plot, you should use a combination of the following: Ice Beam, Grass Knot, Aura Sphere, Thunder, or Dark Pulse. However, Mew is completely and utterly outclassed at sweeping by Garchomp, Rayquaza, and Groudon on the physical side, and Mewtwo, Darkrai, and Latios on the special side. Furthermore, many Pokémon are too powerful for Mew, as its 100 / 100 / 100 defenses just cannot hold up to some of the Ubers sweepers, especially if its already taken damage, causing Mew to Baton Pass out almost immediately. In this case, it would just be better to be a pure Baton Passer.
Checks and Counters
There is no single, undeniable counter to Mew. You have to figure out which one of its list of sets (and possibly those that are not listed) it's using before you can conceivably counter it. And be careful—Mew can Hypnosis its counters.
Metagross serves as a good counter to most Mew, even when Mew has attacking moves, as it can even survive a boosted Earthquake and destroys Mew with Meteor Mash. Likewise, Tyranitar can handle a +2 Aura Sphere and Earthquake, if EVed correctly, but it will fall to a boosted Brick Break. Both can hit Mew with Pursuit if it switches, but it will usually have Baton Pass, meaning it can dodge taking a hit. Thanks to its superior Speed, Mewtwo can use Taunt to shut down any attempts Mew makes to Baton Pass or firing off status attacks.
Since Mew is likely to be carrying Baton Pass, slower enemies will have trouble technically countering it, as it will be able to fulfill its role of passing stat boosts without disruption. With this in mind, sending in a faster Pokémon who is able to prevent this is the best way to stop Mew. Darkrai is a fine choice for this, as is a Taunt Mewtwo. Latios can scare Mew off by threatening a KO from Draco Meteor. Weavile, although not very common in Uber battles, is one of only a few Pokémon who carry a powerful Pursuit and outrun Mew, so it will be unable to avoid the hit by using Baton Pass. Deoxys-A can also pull this off, but it cannot switch into any direct attack from Mew. You must be careful, however, as after a Rock Polish, Mew will outspeed almost every Pokemon, except very fast Pokémon who have Choice Scarf (such as Darkrai, Shaymin-S, and Mewtwo).