Perhaps Percy is driven by a sense of duty. As a hero, he has often been in situations where he has to face great threats. Typhon is just another, albeit extremely powerful, enemy on the list. His past experiences of saving the world from various monsters and gods gone bad might make him feel responsible for taking on Typhon and eliminating the danger he represents.
It could also be out of revenge. Maybe Typhon has directly or indirectly harmed someone close to Percy. For example, if Typhon has caused destruction in Camp Half - Blood or has injured one of Percy's friends in a previous encounter. This would fuel Percy's anger and determination to kill Typhon to avenge those who have been wronged.
One possible motive could be to protect his friends and the world. Typhon is a powerful and dangerous being. Percy might see that Typhon's existence poses a huge threat to everyone he cares about, like Annabeth, Grover, and all the other demigods. So, in order to safeguard them and the world from Typhon's potential destruction, he decides to kill Typhon.
One possible motive could be a sense of betrayal. If the gods had broken promises to Percy or his friends too many times, he might feel pushed to the edge. For example, if they failed to protect his loved ones despite his loyalty and service to them in previous adventures.
One possible motive could be self - defense. Maybe Ares was about to harm Percy's friends or family, and Percy had no other choice but to fight back and end up killing him.
One possible motive could be a misunderstanding. Maybe Hercules is framed for something really bad, and Percy, believing the false information, decides to take action. For example, if there's a plot where Hercules is made to seem like he's about to destroy a city full of innocent people, Percy might feel it's his duty to stop him, even if it means killing him.
Perhaps in the fanfiction, Percy is forced into a situation where he has to choose between Thalia's life and the safety of many others. If the situation is presented in such a way that killing Thalia seems like the only option to save a large number of people, he might be pushed to do it. It could also be related to some prophecy that Percy misinterprets. If the prophecy seems to suggest that Thalia will bring great doom, and Percy takes it too literally, he could end up trying to kill her.
It could also be about power. Percy might realize that with Zeus out of the way, he can reshape the world of the gods in a more just and fair way. He could believe that Zeus's rule is corrupt and that killing him is the only way to bring about real change.
Perhaps Percy had lost someone very dear to him because of Tartarus. This could have filled him with so much rage and a thirst for revenge that he decided to kill Tartarus. In fanfics, emotions often drive characters to extreme actions. Percy, being a hero, might have thought that taking out Tartarus was the ultimate way to avenge the wrongs done to him and those he cared about.
One possible motive could be a misunderstanding. Maybe the Hunt has been misinterpreted as a threat to Percy's friends or Camp Half - Blood. So in his attempt to protect his own, he takes extreme action.
One possible motive could be some sort of mind control. Maybe a powerful enemy has the ability to control Percy's actions and forces him to go after Artemis. This would add an element of tragedy as Percy would be acting against his will.
One consequence could be that Percy gains a lot more respect among the demigod community. Controlling Typhon is no small feat, so he'd be seen as an even greater hero. Others might look up to him more and he could potentially become a leader in a more significant way.
In the fanfic, perhaps Harry had reached his limit with Umbridge's blatant disregard for the rights and well - being of the students and magical creatures. She was a symbol of the corrupt Ministry at that time. Harry, having a strong sense of justice, could no longer tolerate her presence and actions, especially after seeing how she treated his friends and those he cared about at Hogwarts.