The 22nd Amendment specifies that "no person" can be elected president more than twice. I think it would be difficult to argue that a Hulk is a separate person rather than an alternate form of the same person. Apparently some scholars have argued that the alternate personalities of someone with dissociative identity disorder should be legally treated as distinct people, though I don't think that would hold up to medical analysis, since they're really just parts of a single personality that are dissociated from each other.
I think it's more likely that a person with Hulkism (to coin a term, I think) would be seen as a single person with a medical disorder than as two different people. After all, Article II specifies that "The executive Power shall be vested in a President of the United States of America," singular. Two people cannot be President of the United States at the same time, so if a person with Hulkism were legally recognized as two people, they'd be disqualified from the office anyway.