Finally got the badge and I can sort of see why this is a medium badge, although there are still many hard badges that are easier. Max up (get a whitish "shield" around you) and head in any direction away from the center and you should eventually find it around midway between the center and the edge (something like 30 or 40 bubbles out from the center). The monster is difficult to describe but it is quite obvously bigger than the rest of them.
One thing that's particularly annoying is that since kongregate sometimes fails to register your achievements you may have already fulfilled the requirements for the badge without getting it. And since you don't know beforehand what the biggest monster looks like you may continue on for hours trying to find a bigger monster to kill.
 "The most 5star rated game about cats sitting on tables"){kind=icon}
 "Idiot Quiz"){kind=icon}
 "Road of the Dead"){kind=icon}
 "Bubble Tanks"){kind=icon}
 "P.O.D."){kind=icon}
 "Plinge"){kind=icon}
 "Take Something Literally"){kind=icon}
 "Asteroid Defense"){kind=icon}