While not technically story-related, I don't believe it is possible to complete the game without unlocking this, as there are over 40 levels and you NEED to get a daisy on each one to finish the level. However, it is worth noting that like all of the collectible achievements in the game, this appears to be cumulative and you may unlock this earlier than Level 40(on my first recording of my Achievement Walkthrough I unlocked it on Level 38) if you have replayed entire levels and collected the daisy again.