Detestably tells you how something is done, or how far it goes: in a way that is very bad and deserves to be criticised or hated. He behaved detestably means the way he acted was that bad. It is the adverb from detestable, and it is formal; you will see it more in writing than in chat. The filed meaning is that same strong blame, only now it sits on the action or the degree, not on the thing itself. Though actually, students sometimes use it as if it described a noun. The thing is detestable; the action is done detestably.