Challenge levels are unlocked once you have solved the first 60 puzzles and all challenges will be unlocked after solving 80 puzzlesSeeing as you need to have solved 80 of the 100 puzzles in the game I suggest you perfect all 100 puzzles first -
Details on how here Perfect Puzzler in Crazy Machines ElementsLuckily this trophy does not require you to get a good score, only solve and the meet the requires of the challenge. The videos provided will show you how to get gold but that is not required so feel free to cheat a bit on some of them.
There are 20 Challenges in the game(Credit to all of the various Youtubers for making the following videos)
Challenge Pack: Brainteasers1. Rescue
2. Basketball
3. High Five
4. Dynamic Bridge
http://www.youtube.com/watch?feature=player_embedded&v=j...5. Separation
Challenge Pack: Braintwisters6. Burning Countdown
http://www.youtube.com/watch?feature=player_embedded&v=S...7. Labyrinth
8. Power Plant
http://www.youtube.com/watch?feature=player_embedded&v=R...9. Shards
http://www.youtube.com/watch?feature=player_embedded&v=3...10. Order
Challenge Pack: Brainstumpers11. Ignition
http://www.youtube.com/watch?feature=player_embedded&v=y...12. Aim Challenge
13. Timing
14. Racing Line
15. Challenge Superball
Challenge Pack: Brainmelters16. Shopping
17. Reflections
18. Roadway Damage
19. Bonus Challenge
20. Clone Factory