Quick analysis on the best Max Shield users
Now that we know what Max Battles will look like in the foreseeable future, I think it is fair to say that having a good Max Shield user might be the most important aspect of winning them. Here, I've listed the bulkiest Max Shield users by the boss move's type (this simplification is useful since the boss is a lot more likely to use targeted attacks and you can switch to a different mon for AoE attacks). We assume level 50 max IV with 3 max level Max Shield (so 180 extra HP, thus bulk = defense * (HP + 180)). The list is cut off at the bulkiest released Dynamax Pokemon species that cannot Gigantamax. (The reason is that Gmax are less accessible such as Lapras.)
Normal/Flying/Psychic/Dragon/Fairy: Metagross
Fighting: Gengar > Haunter > Butterfree > Zapdos
Poison/Rock/Electric: Excadrill
Ground: Articuno
Bug: Moltres
Ghost: Blissey > Chansey > Dubwool
Steel: Suicune > Metagross
Fire: Suicune > Blastoise > Entei > Urshifu-R > Moltres
Water: Suicune > Lapras > Blastoise > Urshifu-R > Venusaur > Rillaboom > Articuno
Grass: Venusaur > Moltres
Ice: Lapras > Suicune > Metagross
Dark: Urshifu-S > Urshifu-R > Machamp > Falinks
For the full list with all max Pokemon that can be released in the foreseeable future along with detailed stats, see this list.
See also this post for the top DPS attackers by type.
EDIT (20250228): Added Suicune, Entei, Urshifu, Chansey family, and Butterfree. Future updates will be maintained here instead: https://gist.github.com/Mygod/4caf6bae721a0d6b1d57615763e96c19