Wiki says: Martian Manhunter possesses a wide variety of superhuman powers, many of which are similar to those of Superman and Wonder Woman, including super-strength, super-speed, invulnerability and flight. Like Superman, Martian Manhunter has "Martian vision" (a term designating both the ability to see through solid objects and the ability to generate optic heat beams).
During the 90s, it was stated that the source of his flight and "Martian vision" is a form of telekinesis (he had occasionally demonstrated more traditional uses of telekinesis to levitate and animate objects during his Detective Comics and House of Mystery appearances).
The Martian Manhunter also possesses the power of shapeshifting, which he employs for various effects (e.g., adopting human or monstrous appearance, elongating his limbs, growing to immense size). He can alter the chemical makeup of his body to imitate various materials such as steel or stone. J'onn can render himself invisible, and is also able to become intangible so as to pass harmlessly through solid objects. He is a powerful telepath, capable of both perceiving the thoughts of others and of projecting his own thoughts. He often acts as a "switchboard" between minds in order to coordinate the Justice League's actions. The extent of his telepathic abilities is great; several times he has connected to the entire planet Earth.
He has demonstrated regenerative abilities, once able to regenerate himself from only his severed hand but with great strain (due to the loss of mass he found it necessary to incorporate new matter from Martian sand). Early appearances of the character show him as able to breathe underwater; the last time he displayed this power was when he encountered Zauriel in the sea of San Francisco in JLA #6. The Manhunter has sometimes been said to possess nine senses, but these additional senses are poorly defined and generally ignored by most writers.
Aside from his superhuman powers, the Manhunter is also a skilled and very capable detective. As Batman mentions in his file, that "in many ways, Martian Manhunter is like an amalgam of Superman and the Dark Knight himself."
__________________ By the power invested in me I now pronounce you DEAD!!!!
Off the top of my head, he defeated Darkseid by taking him to the center of the Source, willed Mars to life again (after The Swarm had destroyed it) after the Source merged him with the planet, and had telepathy so intense that Resurrection Man 1 Million had trouble coping with it from Earth, even though MM was still on Mars.