tl;dr You don't want to play Dark Souls the RPG.
What would a Dark Souls tabletop role-playing game actually look like? I think it would be a d20 rip-off. One of those 3rd edition open game license d20 fantasy heartbreakers that just has some new cover art but is a game you've already seen, already played, and probably already own. The rules were written on the back of a napkin. Somewhere buried back behind the "new" feats and prestige classes is an appendix with the original concept for an alternative way of treating D&D modules, and that's the true heart of the Dark Souls RPG.
It’s basically a way of modifying existing D&D modules and the entirety fits onto one page, but this company paid for the Dark Souls license and that's why you had to wade through a 300-page cookie cutter d20 rulebook with recycled artwork from the Dark Souls Design Works hardcovers to read this one page.
The first time you fight something you don't roll initiative, you get to go first, but you need to roll a 20 to hit. If you miss your roll then your number to hit that creature decreases by one permanently. Example: If you fight a skeleton you need to roll a 20, and if you don't roll a 20 then that number decreases to 19, and then the next time you attack if you miss that number decreases again, perpetually, every time you miss, until you just always hit the skeleton.
That skeleton you're fighting though? It ALWAYS hits you. And you have as many hit points as your level.
You don't roll damage, instead it is a reflection of your level versus your opponent's Hit Dice. You need to hit them a certain number of times based entirely upon their Hit Dice divided by your Level, plus one. Example: If a skeleton is 1 Hit Dice, then at 1st level you need to hit that skeleton twice in order to kill it [(1÷1)+1=2]. Dividing always rounds to the nearest, so at 2nd level you still need to hit a skeleton twice (1÷2=0.5) but at 3rd level you only need to hit the skeleton once (1÷3=0.3). All of this means that combat in the Dark Souls RPG is very tedious and boring.
You can probably have a simplified version of this where PCs only track their To Hit numbers versus the number of Hit Dice a monster has. Thus, instead of tracking what you need to roll against a skeleton, you track what you need to roll against any creature with 1 Hit Dice, but your character sheet would just be a list of what it takes to hit creatures of different hit dice levels.
And death, every time you die the module resets and you return to where you last rested. The GM would have to either include bonfires in modules or just have designated resting areas. An entire party of PCs could work, if they are able to avoid a Total Party Kill (which repopulates the whole map) and at least one PC survives the battle then the other characters could be "summoned" back, but only survivors receive XP.
If you have a spell instead of attacking then you can avoid rolling dice to hit, but you’re still going get hit, especially by ranged attacks.
How do you level up? I don't know, probably the usual D&D way. I didn't think that far ahead. The point being: Dark Souls makes more sense as a video game, it doesn't make any sense as a tabletop RPG.
That’s pretty much the whole idea, but this sprung out of the idea that if you’re playing a role-playing game and you’re taking on a particular role you should be really good at that, right? You don’t want to play Dark Souls the RPG because it is as boring as it sounds.