The answer to this is "like" and not "as." The simple reason (there is a more technical one) is that "like" is a preposition linking nouns, and "as" is a preposition linking actions (verbs). "Hell" in this case is a noun, and you are comparing the state of something to another state. If you use "as" instead of "like," then you are comparing the action of "to hell" with "hurting." Grammatically speaking, you cannot do that because "hell" is not an action.

I agree with Richard - you should use "like" for this phrase. In spite of that, you will see examples of "hurts as hell". There are basically two reasons: 1) it's easier to say; and 2) you have an implied verb. "It hurts as hell does." These examples are fairly rare, by the way. So, stick with the clear English rules ("hurts like hell") and you'll have no problem at all.