The Manhunter from Mars is an alien, even more than Superman is. Clark Kent was raised as a human, and even his knowledge of his alien heritage does not make him think or feel less as a human would. J’onn J’onzz came to this world as an adult, fleeing the greatest trauma he had ever known, the sole survivor of his people who had witnessed and felt every single death, including those of his wife and daughter.
He is a philosopher, caring for humanity but also detached by both nature and choice from us. He observes from the outside, seeking always to learn, to understand and to integrate what he has learned and understood. J’onn’s particular kryptonite is fire, and unlike most of us, J’onn has made a long study of his kryptonite, and repeatedly attempted to cure himself of it, with not inconsiderable (if impermanent) success.
The Martian Manhunter’s method of dealing with kryptonite is the considered combination of all the methods of his fellow Justice League members. He applies his will, uses his endurance, conducts research, seeks advice, and meditates upon the truths he learns until they resonate in his heart and soul, with an intellect that is vast and cool, but ultimately sympathetic. And then he takes action. Firm, decisive action.
And in the end, that’s the only way of beating kryptonite. No one ever said it would be easy.