There are some places where you will be completely unprepared. A good option is to use the defense break arts that reflect damage back. During some boss battles I would do no damage at all even on their weak spot. My advise is to raise risk as high as possible so your heal spell is the most powerful. The higher the risk the more you cure for. Then time it right and reflect the damage he does to you back on him.

As for knowing what a monster is weak for, unless you skim ahead in guides you will most likely not know.