Pay attention to the "action cast bar" next to the bosses hp bar. It only appears when the boss starts to cast a action.

If a bosses hits you with a action that only hits you and does alot more damage than the other actions it's doing, that's usually the tank buster. Just try to take note of what that action is called, and the next time you see it being cast prepare for it with a defensive action of your own.

Alot of bosses have patterns, and you'll learn those patterns from experiencing the fight more often.