Mew is a very versatile Pokemon with a nice type, a good bulk of 100/100/100 and a huge movepool, being able to learn every TM, HM, TR and Tutor Move. With the cut Pokemon in Sword and Shield, Mew lost several of the counters it had in the last generation, with only Weavile, Sableye (which lost its Mega Evolution), Tyranitar, Gengar, Mimikyu and Reuniclus remaining. Even if it has the Synchronize ability, which makes it able to share status conditions with its opponent, and with Toxic not being a TM anymore, Mew has to avoid status conditions as much as possible. Mew is able to decide its counters and checks depending on the set it carries thanks to its balanced stats of 100 and its movepool.
Physical Attacker
Move 1: Dragon Dance / Swords Dance Item: Life Orb / Lum Berry
Move 2: Psychic Fangs Ability: Synchronize
Move 3: Close Combat / Drain Punch / Fire move Nature: Adamant / Jolly
Move 4: Play Rough / Agility / Roost EVs: 252 Atk / 4 Def / 252 Spe
Moves
Dragon Dance is used as setup move that boosts Mew's attack and speed. Swords Dance duplicates Mew's Attack, however it would loose the speed boost that is really nice as Mew has only a decent 100 speed which makes it easy to outspeed. Psychic Fangs is Mew's best Psychic physical move which also destroys screens. Close Combat is used for coverage against Steel and Dark types and also gives coverage against Normal, Ice and Rock types, a +1 Attack Mew can OHKO a 252 HP / 252+ Def Tyranitar with this move; alternatively, you can use Drain Punch which has less power and wouldn´t OHKO Tyranitar, but doesn't lower your stats and can help you to recover some Life Orb damage; you can also run a Fire move like Flare Blitz or Fire Punch instead for Ice, Grass, Steel and Bug coverage, covering 1 weakness and 1 resistance. Play Rough as a last move brings coverage against Dark/Ghost Pokemon that are inmune to both of Mew's attacks and +1 Attack Mew is able to 2HKO a 252 HP / 252+ Def Grimmsnarl-Gmax or Sableye, if you are running Swords Dance, you can carry Agility instead of Play Rough doubling your speed, but remember Mew will probably only be able to use a Setup move once. Roost can also be used to restore HP if you are using Dragon Dance and have Pokemon like Sableye or Grimmsnarl covered.
Set Details
If you are using Dragon Dance, you can use an Adamant Nature as you will be able to boost your speed with this move, if you are using Swords Dance + Agility, you must use a Jolly Nature, as Mew will probably only be able to use once its setup move. Life Orb is used to boost Mew's attacks in exchange of a little of Mew's HP, which can be covered using Drain Punch and/or Roost, you can use Lum Berry to avoid status conditions, specially being burned which is a good way to counter this set.
Usage Tips
If you are using Swords Dance + Agility, use Swords Dance against Stall/Defensive teams, as Mew acts very good as a Wallbreaker against this kind of teams, but use other Pokemon to cover Sableye and Grimmsnarl and other Pokemon Mew won´t be able to deal enough damage for. If you are facing a more offensively oriented team, using Agility is a better option, as it is important to outspeed other Pokemon that can threaten Mew with their STAB moves. Find the best Setup opportunity for Mew after the opposing team has already been weakened and Mew's threats, checks and counters have been covered. Use Roost to be more long-lived and have more chance to sweep.
Physical Attacker
Move 1: Dragon Dance / Swords Dance Item: Life Orb / Lum Berry
Move 2: Psychic Fangs Ability: Synchronize
Move 3: Close Combat / Drain Punch / Fire move Nature: Adamant / Jolly
Move 4: Play Rough / Agility / Roost EVs: 252 Atk / 4 Def / 252 Spe
Moves
Dragon Dance is used as setup move that boosts Mew's attack and speed. Swords Dance duplicates Mew's Attack, however it would loose the speed boost that is really nice as Mew has only a decent 100 speed which makes it easy to outspeed. Psychic Fangs is Mew's best Psychic physical move which also destroys screens. Close Combat is used for coverage against Steel and Dark types and also gives coverage against Normal, Ice and Rock types, a +1 Attack Mew can OHKO a 252 HP / 252+ Def Tyranitar with this move; alternatively, you can use Drain Punch which has less power and wouldn´t OHKO Tyranitar, but doesn't lower your stats and can help you to recover some Life Orb damage; you can also run a Fire move like Flare Blitz or Fire Punch instead for Ice, Grass, Steel and Bug coverage, covering 1 weakness and 1 resistance. Play Rough as a last move brings coverage against Dark/Ghost Pokemon that are inmune to both of Mew's attacks and +1 Attack Mew is able to 2HKO a 252 HP / 252+ Def Grimmsnarl-Gmax or Sableye, if you are running Swords Dance, you can carry Agility instead of Play Rough doubling your speed, but remember Mew will probably only be able to use a Setup move once. Roost can also be used to restore HP if you are using Dragon Dance and have Pokemon like Sableye or Grimmsnarl covered.
Set Details
If you are using Dragon Dance, you can use an Adamant Nature as you will be able to boost your speed with this move, if you are using Swords Dance + Agility, you must use a Jolly Nature, as Mew will probably only be able to use once its setup move. Life Orb is used to boost Mew's attacks in exchange of a little of Mew's HP, which can be covered using Drain Punch and/or Roost, you can use Lum Berry to avoid status conditions, specially being burned which is a good way to counter this set.
Usage Tips
If you are using Swords Dance + Agility, use Swords Dance against Stall/Defensive teams, as Mew acts very good as a Wallbreaker against this kind of teams, but use other Pokemon to cover Sableye and Grimmsnarl and other Pokemon Mew won´t be able to deal enough damage for. If you are facing a more offensively oriented team, using Agility is a better option, as it is important to outspeed other Pokemon that can threaten Mew with their STAB moves. Find the best Setup opportunity for Mew after the opposing team has already been weakened and Mew's threats, checks and counters have been covered. Use Roost to be more long-lived and have more chance to sweep.