NOTE: Pokémon Sword or Pokémon Shield are REQUIRED to get the quest. If you don't have save data from either, you cannot obtain Shaymin in Legends Arceus.
It spawns in the Obsidian Fieldlands. There's a special request you get from Laventon's blackboard about giving thanks and it leads you to the Floaro Gardens area in the Fieldlands. When you're there you have a brief cutscene and then Shaymin appears. After the quest completes, you can catch Shaymin. Not too hard, thankfully.
Update: Caught Tornadus, I feel like my lung capacity has decreased by about 2%.
Yeah, no. I mean this as respectfully as I can say it: whoever on the development team designed those nightmarish encounters should not be allowed to come back. Those fights are not fun in the slightest, and I have more fun trying and failing to find a shiny Hisuian Zorua. Landorus was surprisingly easy compared to its brethren, but dear god, please do not let any other Pokémon game have encounters that are THAT bad. I know Enamorus is the last one, but I'm only going to full-catch the dex once for Arceus. After that I will reset and I will not be bothering to try a full completion SOLELY because of the Forces of Nature.