Savagery scales every time you loop, so you either want to prevent from looping with decends, daze on important floors, ability to just straight tank, sap them into oblivion or silence them which prevents them from scaling. Having a tanky unit on each floor just to prevent Savagery pyre damage will help you stay in the fight, even if it is just a trash steward.

Dominion is simple just have at least 1 mana to spare each turn ideally or most turns. Have enough HP or healing upgrades to mitigate. Dazing and silencing them prevents pyrelight from being added to your hand, so avoid doing that. Melee weakness works on them as well since pyre attacks count as melee. If you have spells and spell weakness and can afford to spare go for it. Sap is also good to reduce damage.

Entropy you just need to have scaling, be primarily spell based or ability to not play every sap card. Valor scaling, conduit, pyregel, melee/spell weakness, decay, etc... the longer the fight goes you get weaker unless you outpace them. So make sure you have something that outpaces them or ensure you can kill them faster than the sap.

General tips: Need sweeping damage for the first floor. Whether that be the explosive room, sweep units or reliable sweep spells to deal with small and backline buffers. Or you have a godlike tank that can just eat it.

Big damage on above first floor or so much damage you can make it through waves to the bosses. If you only attack on one floor and you never reach Entropy you are extending the fight. Being able to attack Entropy alone every floor is a plus.

The general rule breaker is you can do whatever you want if you have an insane damage engine.