One of the rarest Shiny Pokemon, get yourself a Shiny Mew! You can choose to get one from Emerald’s Faraway Island or one from the Virtual Console games.
The VC one will come with the Gameboy (GB) marking and can only be traded to Pokemon Sun/Moon and Ultra Sun/Ultra Moon.
You can choose if you want the Pokemon to come Battle Ready/Fully-Trained or untouched in the state it was received, and if it is to be Shiny or not. No further customization is possible.
This can be purchased for Pokemon Ultra Sun and Ultra Moon, Sun and Moon, X and Y, Omega Ruby and Alpha Sapphire.
In USUM, you can receive the Mewnium Z-Crystal by taking Mew to the NPC in Heahea City’s Tide Song Hotel.
Pokemon will be sent via Wi-Fi Link Trade in the in-game Festival Plaza or Player Search System. You will need to catch junk Pokemon to send over in place of what you’re getting. Visit the Trade Guide if you’re not sure how to do this.