In Cut The Rope timing is the key. Bouncy platforms and moving spike rails can undo all of your hard work very quickly. Once you know the moves you need to execute, try doing so as quickly as possible from the start of the level. No luck? Start again but wait a second before starting things off - repeat until you get your timing just right. At the very least this should get you through the levels, even if it means you don't get all of the stars.