Just beat it again. This time by completely rushing it to through the portals and without "Killing" anything. If you don't kill anything with your wand or by kicking before reaching the next portal you'll be rewarded with a free treasure chest in the perk room.
Thing is, trick kills (IE killed by the eviroment, other enemies, objects you kick into enemies) don't count as killing and you can use a tablet to kill enemies by throwing it at it which will count as a trick kill. Still I mostly rushed through and only killed when I needed to.
Thats very interesting. How good were the extra chests? I might have to try this out!
Edit: Extra chests seem to be the same as regular chests. I've gotten hearts and spells so far. Killing with trail effects seems to count as well. Update: The clear condition seems a little bugged, even when I killed nothing and ran straight down it only works half the time. The enemies will kill eachother and one of their kill conditions might break it. It might be pheromoned enemies counting as your kills.