How does the damage resistance on Hush work, and how can you overcome it?

According to this reddit post, the way it works is that those bosses record how much damage they take and adjust the resistances accordingly.

So if you deal a huge burst of damage all at once, they'll greatly increase the resistance.

Knowing this, the best way to deal with it is either deal bursts of single instanced damage once in a while or attack for a few seconds, stop to let the resistances fall off then attack again.