Ok, first of all I write this solution, becouse i want to get the achievement '
Challenge Accepted' for
TA app and this challenge at the same time.
I started the game just yesterday and saw there is no guide for this challenge.
I've already completed 9/10 levels with no death, and my strategy was first to play every level at least once so i know what to do, and then replay the level with no death.
Believe me, there is not an easy way to do that, some time i can beat the level from first time, but other time died a few time and replayed again.
I believe this levels are not that hard for the challenge:
Chapter I 1-2: Anotherland;
1-3: Sea of Sand;
1-4: Black Rock Canyon;
1-5: The Crossing;
Chapter II2-1: Roots;
2-2: into the Wild;
2-3: Father Oak;
2-4: Tomb of the Giants;
Chapter III 3-1: Lost in the Dark;
3-2: Lantern Bugs ... just writing the solution before completing this level :)
....and 20 mins later..
DING... both achievements unlocked!
Edit: When you finish any level without dead a
skull icon will mark that level, so you can check that from Chapter Select and you will know that this level is completed with no dead.