Yo,
In expansions past there were certain “checks” during boss fights that would require you as a tank to use a very specific ability to pass the check. It’s a mechanic. This is not a question about brewmaster AM but instead about this mechanic.
Think back to legion with the final boss of Neltharions layer, Ularogg I think. He would cast an ability that would knock tanks back and cause a lot of damage. To pass this “check” mechanic, every tank had a very specific predetermined ability to use which would prevent the knockback. This ability was always part of their active mitigation toolkit.
What is it for brewmasters right now?
It was Ironskin Brew, it was removed in Shadowlands and baked into our rotation, it’s currently shuffle and on live it’s passable to somewhat decent as a defensive.
Though do mind there’s a hidden k value that deducts shuffle and armour value that’s shown on your charactor sheet when you’re in a key or raid.
As of now, Stagger works like that, though the big hit is still there and can be absorbed well with Celestial Brew.
If you BoK inti Celestial you get a pretty hefty shield. Purifying Brew to smooth out your stagger intake afterwards.
For real big hits you can Fortifying Brew, although its a 4 minute CD.
For Ularogg, Celestial Brew works fine, but you still have to roll back as there is not avoiding the knockback anymore from what ive seen.
If its just about avoiding the knock back you can always just use transcendence to teleport back after receiving the knockback.
The rest of your question is a bit more vague but I think if you aren’t asking a class related question and are asking about mitigation check mechanics in fights, then you may have slipped accidentally into the wrong thread. Right now we are in Classes>Monk>.
If it is about BrM then your active mitigation is shuffle/stagger/purifying brew, and your deliberate mitigation tools are diffuse magic, dampen harm, ironskin brew, zen meditation, Niuzao, celestial brew. We also have our passive mastery which is pretty average that increases our dodge.
These checks don’t exist anymore.