It's a common theme in all three Kung Fu Panda movies: the villain believes they're destined for greatness, and is willing to steal everything from others in order to gain that greatness. Meanwhile, Po achieved greatness all on his own through confidence and skill and humility.
Tai Lung sought to be the Dragon Warrior because he believed it was his destiny- a destiny that Shifu instilled into him. It was only when Po revealed the secret of the Dragon Scroll to Tai Lung that he finally realized that the Dragon Warrior was not something one could become, it was something one was.
Shen was raised as prince of all China, and believed that he was destined to rule it all when he grew up. He believed that his ruling over China was the most important thing ever- and so when his family's soothsayer foretold that he would be cast down by a warrior of black and white, Shen ordered a genocide against his own subjects. He genuinely believed that his throne was more important than the lives of thousands of people.
Kai the Collector was a great warrior who fought alongside Oogway, but when he learned the secrets of Chi manipulation, he used it to steal chi from others in order to make them his slaves. He readily threw away the lives of everyone he met, growing in power by stealing the very souls of his victims.
Po defeats his foes not by being superior to them in body or skill, but by being superior to them in spirit. He defeats Tai Lung through self-confidence and determination; he defeats Shen through learning to accept what he can and cannot control; and he defeats Kai by learning to accept his past, present, and future.