The most useful monster.

I don't know about online play. As for why these monsters are useful in offline mode, I've indicated it in parentheses. Here's an example. Let's say there's a group of 5 Dungeon creatures. I attack with one Fairy and win :) This is a legitimate tactic in offline mode. I find a good spot for the Fairy and slowly wear down the enemy, using save-loading to manage morale. You'll agree that this won't work online.