Since there's no tricks to get this outta way of a 100% completion, the only way is to knock it off is with some skill. Here's my 2 cents of advice:
1- Get the other 12 achievements done before attempting this one. For one, it will motivate you more. Besides, only one of them is somewhat challenging. For two, you won't be distracted nor worry about collecting eggs or anything else;
2- If you don't want to spend time practicing the last levels for an unknown amount of time, I suggest you start a new game and see how far you can get without dying once.
When you die, write down what level it was and what was it from. This will help greatly in avoiding the same mistakes;
3- Keep progressing until you die 6 times. Now you have parameters to replay specific levels if you want and also can set a goal to reach that same area with less deaths than the previous time until you can beat the whole game with only the 5 or less. Another good advice is to pause the game every once in a while and see on chapter select what lies ahead to exercise your memory.
If you have no patience for methods like the above, I'd suggest you watch the video below (I got it from Youtube, don't own it) 1 minute at a time (so, in about 60 little parts) and try to follow the example to succeed.