I think I know the two themes to the bosses. They are all members of the Chinese Zodiac http://en.wikipedia.org/wiki/Chinese_zodiac and the items you obtain after defeating them are birthstones. http://en.wikipedia.org/wiki/Birthstone
Now I know why it's not getting badged. It's because the developer didn't add Kongregate API, so the game can't be badged. So if you want badges upvote this comment and tell developer to ADD KONGREGATE API so we can get badges.
@goldslash The quality buttons show up if you right click in the preloader (worked for me at least). For some reason it wouldn't show during game play though :(.
I wish there were a way to tell which fox you still need clothes from during your run, like having that fox glow red or an exclamation mark over his head or something.