Special Quests

The manual mentions that there are 'Special Quests' for each level.  Beyond
this brief note, there is no hint at all that these even exist.  Completing
each one gives you additional experience points, and some of them give you a
few extra items.  Only the Special Quest for the last level is even really
hinted at elsewhere in the game.  As a result, the following hints don't
bother being subtle; they just tell you what you need to do on each level. 
So if you want to try figuring them out for yourself, you've been warned not
to peek.