In Pokémon Legends Arceus, You need to complete the pokédex in order to meet Arceus. But since Shaymin and Darkar are special events which you can only get if you have a save file of sword/shield and BDSP. Do you need to catch/trade them to complete the pokédex or are they exceptions?
The short answer is No.
As both Pokemon can only be caught during the main story by having save data from other games, Shaymin and Darkrai do not count towards Pokedex completion in Pokemon Legends: Arceus. Which makes quite a lot of sense, considering it wouldn’t be fair to force players to purchase other games just to complete the new one.
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