All shiny-locked Pokémon in Legends Z-A are listed below:
Static Encounters:
All static encounters, such as Legendaries/Mythicals (all of which are Static in PLZA) and Your Starter/First Partner Pokemon are Shiny Locked. However, Starters found in the wild, postgame, are not Shiny Locked.
In-Game Trade Pokémon:
All in-game trades are Shiny Locked, meaning regional variations (among other things) that can only be obtained via in-game trades can’t be Shiny.
Pokémon Obtained Via Mystery Gifts:
All Pokémon obtained through Mystery Gifts, such as the Ralts obtainable from having pre-ordered the game and the to-come legendaries from quests, are Shiny Locked.
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Tell me in the comments If I missed anything please!