From the Super Mario Wiki
Behemoth King is a more challenging version of Behemoth, who is encountered in Sports Mix mode of Mario Sports Mix, thus making Behemoth King the game's second and final boss. It is fought when the players' team beats the Final Fantasy team (consisting of either just Ninja and White Mage when playing with 2 characters, or both with Black Mage when playing with 3 characters) and obtains the luminescent crystal. The events that follow this are not vastly different with the precursor to Behemoth; once the crystal gets placed, it turns dark and drags the ship into a portal, which the players' characters encounter. The crystal materializes into Behemoth King instead of Behemoth however.
Behemoth King has a slightly different attack pattern, and it is more resilient to attacks than Behemoth. Other than this and its color swap, there is little to no difference to Behemoth.
The Behemoth King, before the boss fight.
The Behemoth King, during the boss fight.
The Behemoth King's icon.
Names in other languages
Behemoth King on the Final Fantasy Wiki