In order to access a time challenge, you must first complete its episode in the story mode. You can then access the level to replay Story or in Time Challenge mode. There are sixteen Time Challenges that need to be completed to unlock this Achievement.
There are numerous videos on the web from 360videoguides that can help through the individual challenges. Some of them are easy once you learn the best route, but others can still pose a challenge.
The most frustrating one from my experience was Happy Happy Fun Fun Game (not much margin for error, and some tricky platforms to hover onto). But any of the challenges can be beaten if you just stick with them and practice.