In the new Godzilla, Godzilla is said to have feed off radiation and hibernates in modern times, feeding off radiation from the core as there is no longer enough radiation in the modern world to satisfy him. Yet the scientists describe him as an alpha predator and the M.U.T.O's as his prey, so what's the deal. Can he eat organic matter as well or did he switch to a pure radiation diet in the millennia he was hibernating?
Godzilla is an alpha predator because he's the biggest*, meanest, killingest thing out there, ever, bar none. Something gets uppity on the planet, he rampages through the nearest major metropolitan area to kill it in a 1-2-hour slugfest with ample gratuitous explosions and collapsing buildings.
Consider the backstory as presented in the latest movie: In the ancient past, when Godzilla and his fellow Daikaiju evolved, Earth was highly radioactive (relative to today). They all fed on this radiation, because that's what was readily available; but Earth has since "cooled off" quite a lot, which means scarce food available for these giant beasts. Hibernation is one survival mechanism they evolved to deal with that; killing their competition, thereby ensuring fewer beasts trying to feed on the small amount of radiation still around, is another.
Godzilla has perfected both of these survival mechanisms, making him an "alpha predator" because he does, in fact, kill for food -- it's just that he's protecting his food from other Daikaiju that would eat it instead.
(*Okay, there may have been a monster or two bigger than him, but the point still stands.)
Technically, an alpha predator is an animal that is not preyed upon by any other animal (this excludes parasites). It has nothing to do with how large, vicious, or carnivorous an animal is, although large animals tend to be at the top of the food chain. Humans, chimps, grizzly bears (which are omnivorous), whale sharks (filter feeders) are alpha predators. So if Godzilla occasionally chomps on another monster and nothing specializes in eating godzillas, that would make it an alpha predator.
Godzilla could of been killed by the M.U.T.O's and their thousands of babies if he didn't kill them first. It's either kill it be killed. That's why he didn't eat them. He just killed them before they killed him!
Like what James said. To become an Alpha Predator you have to kill all of the animals that are better than you and Godzilla I think found another Alpha Predator. If the M.U.T.O.s killed Godzilla then the M.U.T.O would be the new Apex Predator or Alpha Predator, but they didn't kill him, Godzilla killed them and now once again Godzilla is still the Alpha Predator.
Maybe because because full grown MUTOs are full of radiation since they feed on it too ? So by killing them Godzilla feeds on natural source of radiation,I mean radiation from living beings.Those were my two cents,they weren't elaborate on that topic in the movie at all,maybe they will explain it better in sequels.