You’ll be able to encounter Amped Form Toxtricity in Pokémon Sword and Low Key Form Toxtricity in Pokémon Shield. If you want to challenge a Toxtricity in the form that you can’t encounter in your game, try joining a Max Raid Battle hosted by someone playing the other version.
To challenge Gigantamax Toxtricity in a Max Raid Battle, you need to have received the latest information about the Wild Area.
You can get the latest information about the Wild Area anytime you connect your Nintendo Switch™ to the internet. Alternatively, you’ll be able to manually download the latest data anytime you want by opening the X menu in your game and selecting Mystery Gift and then Get the Wild Area News.