You can make the run on lvl 14 without the bow, just wait in the hole and time it so you're already running left before the last dude drops down. I thought the bow was a red herring.
YESSS impossible badge is mine. Strangely addictive despite the slippy controls. World 10 advanced is hilarious, took me over an hour to do. It's a shame the trophies are buggy, the one for world 7 finally popped after my fifth run completing without the powerup.