This is unlocked by purchasing the last item you can unlock from the Soul Shop. The main issue with this is the amount of souls you need. You get 800 souls per thread (100 per boss), and once you get all of them from a thread, you cannot get any more from that thread. Just going through threads is not nearly enough if you want this done in a reasonable timeframe.
Fortunately, your main source of souls before endgame (NG+8 and beyond) is a lot more ludicrous. By befriending a character, you get 500 souls. To befriend a character, simply interact with them when they have a ,(...) over their head.
The best method though is going for Purifying Erebus, which requires you to unlock, then find, then complete all scars. The later ones of these give up to 800 per trophy. Some of these are challenging to say the least, so completing red portals you find exploring the dungeon will make this easier, as they add a stat modifier to your character in the scars (at the cost of lowering the score multiplier). Most are manageable without these, however, so feel free to use these buffs at your own discretion. House Rules do stay in effect for scars, if you want to use that to make it easier.