Hulk is simply not immortal

Let's discuss this for a moment. Please correct me if I am wrong, but I do not know of the Hulk dying in canon, and I do believe that he has been shot in the head in human form. This implies that he can hulk-up faster than a bullet to the brain can kill him. I do not know much of Kratos's power, but I do not think he has any abilities that can kill Banner faster.

This means he will be fighting the Hulk already in green-mode any way you cut it. Now let's assume that Hulk's healing powers, size, and strength all increase whenever he gets madder, and that he gets madder whenever something or someone manages to injure him in Hulk form. If Kratos can kill him instantaneously, this point is moot, but if the god's chosen attack takes time to reap mortality, and I believe his usual weapon is a blade, so that would be a yes, then the Hulk can increase in power and healing factor before he succumbs to said wounds.

Now, we know that Hulk freely and regularly defies the laws of conservation of mass and energy that things in our universe have the decency to conform to, but we must ask if this ability is unlimited. Can the Hulk, for example, continue to hulk-up more and more until nothing is big enough to make him angrier, or is there a set limit, such as city-size? If the latter is true, and Kratos is truly immortal, then Kratos would win, eventually taking down a preposterously large and powerful Hulk.

If the prior is true, however, and if Kratos is truly immortal, then this fight would be a true draw with the two of them duking it out until Hulk was the size of the universe. Picture universe-Hulk futilely crushing Kratos between his fingers, and the unscathed Kratos delivering galaxy-destroying blows to the inside of Hulk's fingerprint.

If Kratos is not truly immortal, and issue which I do not know enough about to discuss, then the latter scenario would easily end in Hulk's victory, possibly at the cost of the Earth's destruction, and the prior would be a fight we would all like to see, at a safe distance, of course.

TL;DR Depending on the limits of Hulk's powers, he might be effectively immortal.