His soul should manifest in a body once in awhile to try and take revenge on you after you beat the game. Each time you defeat him, he would blow up again. His hatred and anger seems too strong, he could send in avatars of himself when he manifest, maybe calling them hatred of alduin or alduin's malice, something like that.

Maybe he could also try different ways to come back and kill you like possessing a npc or something. Each time he comes back, he would atack different locations to try and lure you there, hoping to kill you. Locations could be Throat of the World, cities, forts etc. Watch out he has a grudge against you.