Well probably anything, except you'd have to do whatever it is a hell of a lot. If we take the game into consideration, then sharp things, bullets, demonic magic, and other such demonic weaponry can kill Dante. Anything human based is suppose to have less effect on weakening him. Thus I would say it would have to be of demonic power to kill Dante. Anyone or thing wielding a weak amount of Demonic energy is not going to slay Dante. Unless he should be totally set upon by demons, he would be ripped apart. However, he out skills all of them. In such case, one like Nero, Mundus or Vergil would be the only such being that could kill him off. Yet the fight would indeed be epic. If we take the fact that Dante needed the perfect amulet and Force Edge's True Form in order to defeat Mundus. Without it, Dante could have faced his death.
So that is your answer. You could indeed burn Dante, but you'd need to roast him for ages; because he won't burn so easily. It's all about endurance with him, someone capable of keeping up with his skill and pace. Without the essential skill, nothing can kill him. He is thus far a deadly, truly masterful, energetic thrill ride of a character.
These are all just my points, and my opinion. Nothing to base this whole question on, or deem as a reasonable answer.
~LoD