The National Dex is very easy to get in this game. You need it to progress further in the game too so here is how to get it:

Meet the Following Criterea:

  1. Beat the Elite Four
  2. Have at least 60 Pokémon in your Pokédex
Then go to Oak's lab and he'll give you and your rival the National Pokédex. Simple

In this game, the National Dex holds the data of Pokémon 152-386 and is necessary to evolve certain Pokémon and to Progress to the rest of the islands

 
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