This page explains the requirements and steps to get the Shiny Charm in Pokémon Legends: Arceus.

Requirements for Obtaining the Shiny Charm

To get the Shiny Charm, you will need to reach Research Level 10 with pokémon 001 through 240 in the Pokédex.

Where to Get the Shiny Charm

If you have reached Research Level 10 with pokémon 001 through 240 in the Pokédex, go to Jubilife Village, enter Galaxy Hall, and talk to Professor Laventon to receive the Shiny Charm.