In a kratos vs naruto fanfic battle, Naruto might have a chance if he uses his strategic thinking. He could use his shadow clones to surround Kratos and then attack from all sides. But Kratos is no pushover. His experience in combat is vast. He has fought against opponents with all kinds of powers. If he manages to break through Naruto's clones and get to the real Naruto, it could be over. However, Naruto also has his sage mode which gives him enhanced strength and perception. So it's a very tough call.
One idea could be a battle in a neutral dimension. Kratos, with his brute strength and god - slaying weapons, faces Naruto's ninjutsu and his ability to summon powerful creatures. Another idea is that they are forced to team up against a common enemy that threatens both their worlds. They start off clashing due to their different fighting styles and beliefs but gradually learn to work together.
Some of Kronos' minions, like the monsters he commands, could be antagonists. For instance, the dracaenae. They are always eager to prove themselves to Kronos and might see Percy as competition within Kronos' ranks. They could constantly try to undermine Percy's position and cause trouble for him.
To develop the character, start with his backstory. Since he's the son of Kronos, he might have grown up in a very different environment compared to other demigods. Maybe he was hidden away by a minor god who felt sorry for him. His past experiences of being alone and shunned because of his father would shape his personality, making him a bit of a loner at first.
Kratos is incredibly powerful, but it's hard to say if he's the absolute strongest. Different fictional universes have their own mightiest characters, and it depends on various factors like their powers, skills, and the context of their stories.
The story of Kratos is complex and compelling. He was once a servant of the Greek gods but was betrayed and wronged, leading him on a violent path. As the series progresses, he grapples with his actions and tries to find a way to atone for his sins.