Following the death of their beloved mentor, three warriors from rival kingdoms join forces to battle against a dying Prince who declares war upon his entire generation.

As mikepedley85 said. The death of the mentor may be a set back but it doesn't seem to qualify as the inciting incident.

And what's the villain's motivation?

And the villain has the strength and stamina to fight a genocidal war even though he's dying?

And the warriors are from "rival kingdoms".? So are they outsiders to the kingdom of the evil Prince?? And if so what is their skin in the game?? Why MUST they put aside their rivalry and meddle in the internal affairs of another kingdom?

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As mikepedley85 said. The death of the mentor may be a set back but it doesn't seem to qualify as the inciting incident.

And what's the villain's motivation?

And the villain has the strength and stamina to fight a genocidal war even though he's dying?

And the warriors are from "rival kingdoms".? So are they outsiders to the kingdom of the evil Prince?? And if so what is their skin in the game?? Why MUST they put aside their rivalry and meddle in the internal affairs of another kingdom?

?

Surely the inciting incident is the moment the dying prince declares war?? What bearing does the death of the mentor have on the story? The inciting incident is the moment in the hero's life that upsets the balance in their life and provides them with the goal of trying to correct this imbalance. If their goal is to defeat the prince, then the inciting incident MUST relate to the prince.

If the prince is dying anyway... how long's he got?

It sounds like these three warriors are the only people fighting against the prince? Is that the case? Or are these three like generals and they combine their armies?

Why does the prince declare war upon his entire generation? It sounds a bit "evil for the sake of evil" and two dimensional. Maybe unpack this a little.

I would recommend choosing one of the three warriors to be the protagonist. Consider Jaws. Whilst there are 3 main characters (Brody, Quint, and Hooper) the story is told from Chief Brody's perspective. All three characters have very different reasons for wanting to kill the shark but their goal is ultimately the same. One of your warriors needs to be the emotional conduit for the audience as this will help them to connect with the story as a whole.?Since your three warriors are rivals, despite being trained by the same guy, they surely have different approaches, ideologies, morals, and ethics?

Hope this helps.