Shiny hunting is one of the biggest post-game activities for Pokémon fans, but not all methods are viable depending on what game you are playing or when you get around to playing it.
At launch, Pokémon Legends: Arceus won’t be a friendly place for players who were hoping to Shiny hunt Pokémon involved in the game’s story, as every static encounter available at launch is listed as Shiny locked. This means no matter how many times you reset the game before starting the encounter with a Pokémon, if it is scripted to appear in that location or part of the story, it won’t be Shiny—unless the script involves a Pokémon Shiny.
This includes all Legendary and Mythical Pokémon featured in the base game at launch, such as Dialga, Palkia, Arceus, and more. This stands true across missions in the main storyline and side quests too.
Essentially, Game Freak has made it so only Pokémon that appear in the wild repeatedly throughout the game can be encountered as a Shiny, which also plays into how the Shiny odds and bonuses have been changed around for Legends: Arceus too.
This method of Shiny-locking was likely done to keep the appearance of said static encounter Pokémon consistent in cutscenes and scripted portions across all games since Shiny Pokémon can appear in the overworld in Legends: Arceus.