His character could develop in many ways. With this new strength, Naruto might start to feel a greater sense of responsibility. He'd be aware that his actions have more impact because of his strength. He could also become more empathetic as he realizes that not everyone has such power and he should use it to protect the weak. He might also face challenges in controlling his strength, which would teach him patience.
Naruto would likely become more confident. His Hercules strength would give him an extra boost in battles and he'd start to believe in himself even more. He might also become a bit more reckless at first, thinking his strength can solve all problems.
Perhaps it's related to some ancient ninja art or a hidden power within Naruto himself that gets awakened. In the Naruto universe, there are often latent powers waiting to be discovered. This Hercules - like strength could be tied to his Uzumaki heritage or some long - forgotten jutsu. He may initially struggle with this new power, not knowing how to fully utilize it without causing harm to himself or others. But as the story progresses, he learns to master it.
He could become more confident, bordering on overconfident. Since he has unlimited strength, he might not face the same challenges in terms of combat, so his development would shift towards moral and ethical challenges.
Enemies might target him more. With such great strength, he would be seen as a huge threat. Other ninja villages or evil organizations might try to eliminate him or steal his power. He would have to constantly be on guard and develop new strategies to defend himself.
Naruto's character would likely become more stoic. Vergil is known for his calm and collected demeanor, so Naruto might start to suppress his more exuberant emotions. He could become more calculating in battles, thinking several steps ahead like Vergil does when facing his enemies.
Naruto might become more serious. Deadshot is a very serious and focused character. So Naruto could lose some of his goofy and carefree nature and become more calculating in his actions.
Naruto might become more cautious. Dealing with the Daleks, who are extremely dangerous and unpredictable, would force him to think before acting. His normal brashness might be toned down a bit.
Naruto's character would likely become more calm and introspective. He'd focus more on inner peace rather than external battles.
Naruto's ability to use chakra and perform ninjutsu like the Rasengan could be combined with Hercules' brute strength. For instance, Naruto could use his chakra to enhance Hercules' strength even further, or Hercules could use his strength to create a more powerful impact when Naruto uses his jutsu. Maybe Naruto creates a Rasengan and Hercules throws it with his superhuman force.
Naruto's character might become more conflicted. His usual positive and straightforward view of the world could be challenged. He might start to question his own ninja way more often, as Pein's extreme methods would force him to re - evaluate his beliefs about how to achieve peace.
His character might be more hardened. Growing up with Yahiko, he'd be exposed to the harsher side of the ninja world earlier. So he'd be less likely to trust blindly.