Pokémon Home allows players to trade almost any Pokémon with players from around the world using a slightly revamped Global Trade System. But just like the GTS in older games, there are a few notable exclusions from the list that you’re unable to trade.
That list basically only involves Mythical Pokémon from each of the generations that were only obtainable via event or other methods outside of the main game.
Game Freak has done this since introducing the GTS in Pokémon Diamond and Pearl, making Pokémon with the Mythical status something that players have to work for by actually participating in events to catch them. This is due to these Pokémon being considered rarer than any others in the game, even Legendary Pokémon, due to the limited nature of those events and Mystery Gifts.
So when trying to build up your National Pokédex, here are the Pokémon you’ll need to get without relying on the GTS.
Some of them, like Mew and Meltan, are both easy to get through Pokémon: Let’s Go, Pikachu! and Let’s Go, Eevee!, Pokémon Go, or the Poké Ball Plus. But the others are going to take some work and potentially some outside help. And don’t be fooled, because the GTS will still let you request Pokémon from this list even though you won’t actually be able to receive them.
The good news is none of these restrictions apply to normal trades between individuals through Home, so feel free to reach out to someone you know and ask for help in finishing your Pokédex that way. Just be prepared for the grind of finding someone who actually has all of these Mythical Pokémon.