Thanks to the Poké Ball Plus accessory that was made to enhance the catching experience in Pokémon: Let’s Go, Pikachu! and Let’s Go, Eevee!, you can actually still transfer a Mew from the device into Sword and Shield.
This will require you to have both a copy of Sword or Shield and a new Poké Ball Plus that has not been used with a copy of the Let’s Go games. A used accessory might have already been part of a transfer, which will stop you from obtaining your Mew.
If you or someone else already redeemed the Mew included in the Poké Ball Plus, this method will not work and you will need to purchase a new accessory or find someone to trade with in order to get a Mew, since it is not catchable in the game.
After starting Sword and Shield you can go into your settings and select Mystery Gift, which will then have another option called “Take A Stroll with Poké Ball Plus.” The game will then ask you to hold down on the control stick (the middle button) on the accessory until it connects to your system.
After your Poké Ball Plus connects, you should hear a noise from the ball in the form of Mew’s cry. That the device has not been used in a previous transfer and you can now import the legendary into Sword and Shield.
Simply select yes when asked if you want to get the Pokémon out of the ball and you will receive your Mew. It will be waiting in your party if you have an open slot and will be level one when you get it.
Added to that, Mew is not actually in the Galar Pokédex at all, rather it is an added Pokémon that can be obtained, but will not appear in your Dex. There are 34 other Pokémon with the same data classification that cannot be obtained in the game right now, including both Bulbasaur and Squirtle.
The Poké Ball Plus serves no function as a controller in Sword and Shield like it did in the Let’s Go titles. Its only purpose is to allow you to take a Pokémon with you while you aren’t playing the game on Switch.
Unfortunately, the results of this so far seem to have been limited to just finding items by using it, rather than being able to earn your traveling companion some bonus experience on your trips. It is unclear if more functionality will be added at a later date, but for now, that is all you can do.
It is also impossible to use the Poké Ball Plus to transfer Pokémon from Let’s Go over to Sword and Shield. If you try to do that you will be informed that there is data for another Pokémon on the device and asked if it is okay to overwrite the information with your new options.
If you do allow the overwrite, any Pokémon on the Poké Ball Plus will be deleted and cannot be brought back to Let’s Go.