This solution is meant to give you the guidelines for getting this achievement, it is not meant to be highly detailed. To get this to unlock, you will need the following completed:
All story related missions
All hoods discovered
All activities/diversions completed (hellblazing, mayhem, survival, altars... stuff like that)
Challenges DO NOT weigh in to this. That has a separate achievement titled 'King of Hell'.
I would highly recommend working on this achievement alongside the 'King of Hell' achievement. I say this because activities like survival and altar give an easy supply of demons for all your weapon and arcane challenges as they can be constantly restarted. If you beat all of them before working on your challenges, you'll have to raise your notoriety level for a good supply of demons which is time consuming and frustrating.
While the weight of this achievement might make it seem difficult, it really isn't. This game has a short story and the activities are easier to complete than in any previous game I have played. There is even a bonus upgrade that gives you extra time to complete activities. I did not waste the money on it but give it a shot if you are having trouble.
Good luck and please vote and comment!