Their interaction would be tense at first. Young Kratos, full of energy and unbridled aggression, might see old Kratos as a threat or an obstacle. Old Kratos, on the other hand, would be more reserved and cautious. But as they start to communicate, they would find common ground in their shared past and their connection to their family.
To be worthy of Mjolnir in this fanfiction, Harry could have a journey of self - discovery. He realizes that his power as a wizard is not just about defeating Voldemort, but about protecting all beings, whether they are wizards, muggles or Asgardians. He could start to train in Asgardian ways of combat and magic, learning their values of honor and courage. Through this process, he gradually becomes someone who Odin or Thor would see as worthy of wielding Mjolnir.
Kratos might win. He has fought and defeated many powerful gods in his own world. He is not only physically strong but also very strategic. He could analyze the Hulk's movements and find his weaknesses. The Hulk, while strong, is more of a brute force fighter. Kratos could use his Blades of Chaos to keep the Hulk at a distance and then strike when the opportunity arises. Also, Kratos has faced opponents much larger than him before and has always found a way to win.
One possibility is that it could focus on a mentoring aspect. Old Kratos, with all his wisdom and experience, could guide young Kratos. Maybe he'd show him different combat techniques or how to better control his rage. It could also be a story of self - discovery for young Kratos as he sees his future self and realizes the potential path he could take.