So the reason I'm delayed on this is both writer's block, and I made the great mistake of posting the first chapter of my other story Omicron, so now I'm working on both of these.
To answer Flashking: I'm not even going to try and match power levels between Skyrim and Dark Souls, because there's no way to compare the two. It's like Goku vs Superman. Completely different universes with completely different rules. Instead I'm just bending the rules a bit so these fights can take place at all, then estimating the chances of success. I mean, magic in Dark Souls is incredibly power in Dark Souls, and Lightning is the one true weakness Dragon's have. In Skyrim magic is meh, and lightning is the only type of damage Dragon's aren't strong/weak against. I'm trying to create a middle ground here.
And Alduin's invincibility is a plot device, let's be honest. It would be pretty cheap if you found a way to kill him in an earlier encounter and totally derail the story. So in this crossover, Alduin is extremely powerful, but not like Archdragon levels of power, and he's definitely not invincible, although in the context of Alric's battles, the Ashen One can't permanently kill him, because he is unable to take his soul. Prophecy is a bitch. In the next two parts, he will need the Dragonborn's help to kill Alduin.