Howdy,
Great comments, I especially agree with Miles and Turtall.
I think it's a fish that demands respect. Basically, a combination of size (absolute as well as relative within species) and attitude. Anything big is a monster. Anything small and carnivorous is a monster, too. I don't think small herbivores qualify as monsters. It's not mere size, but size certainly helps.
A butterfly fish, going after a cricket, is a monster just like an arowana. Especially if you ask the cricket.
HarleyK