The Shiny Charm is one of the most important items in any Pokémon game because it drastically increases your chances of encountering a Shiny Pokémon in the wild.
Once you obtain the Shiny Charm in Sword and Shield, it boosts your odds from one in 4,096 to one in 1,365.33, the exact same as in X and Y. That is a huge difference, especially if you pair it with things like the Masuda Method or shiny chaining.
Getting the charm is going to be a bit of a slog, however, since you actually need to complete the entire Galarian Pokédex first. That means you will need to have captured and recorded data on all 400 Pokémon available in the game.
That total does not include Dynamax or Gigantimaxed Pokémon because those forms do not have pages in the Pokédex.
Once you have all of the data, head to Circhester and enter the first hotel in the city square. Take the elevator up and enter the room furthest to the left before talking to the doctor NPC at the back of the room.
This is the same NPC that gives you the Catching Charm, which increases your chances of performing a critical capture during battle. So if you have yet to speak with him, you will be given that item first.
He will then prompt you to complete your Pokédex for another reward. Show him your completed Pokédex and he will hand you the Shiny Charm and you can now begin to hunt for those alternate colored mons like a pro.
There are several methods you can use to find the Shiny Pokémon, but at least now you will have a higher chance at doing so if you want to go back and try your luck in the Wild Area again.
