King Leviathans were more strongly armored, and had stronger blaster attacks than the regular Leviathans. They were highest in the Leviathan hierarchy that were native to planet Sarathos. They were also much bigger than normal Leviathans and wore very ornate looking armor. They lived in the Leviathan Lair which was a small arena with a pool in the middle which one came out.
It also appeared that there was more than one King Leviathan, as later on in the game, more could be found in the DreadZone challenges, although they were rather uncommon and not as resilient as the Sarathos King Leviathan.