After reading the Lumber Challenge thread http://forums.spiralknights.com/en/node/53915 I thought that maybe we should implement challenges in Missions as optional Sub Missions in a sort of "Wario Land: The Shake Dimension" fashion. Sub Missions can be unlocked after completing the mission once and should reward players with extra crowns, prestige and/or rare materials. I believe this may encourage players to revisit previous mission and challenge themselves in case they get a bit bored of farming boss levels.

For example we could have sub-missions where we have to prevent being hit a certain number of time, finish a level in a certain time limit, cut an x number of bushes, kill an enemy with a pot, extinguish y number of shadowfire etc.

However there should also be some unique sub-missions to vary things up a bit. One idea that I have is to lure a set number of a certain monster (maybe gold monsters perhaps) into a holding pen in the level for Biotech Hahn to carry out his studies without killing them, like the previously mention Lumber Challenge.
Another idea I had was to have missions that restrict the use of certain types of weapons as in "Only use bombs on x level", "Use guns on y level" or "Only use piercing weapons in the Jelly Palace" to provide a bit of challenge.

That's all I can come up with at the moment so feel free to expand on these ideas below if you want. Constructive criticism would also be appreciated.