There are a total 4 unlockable levels. One for each world. You will have to complete the respective world and collect all coins to unlock the specific level.
You can start with the levels right after beating the boss of a world. You do not have to have the game completed beforehand.
You can select the level via the world's map. It is always right behind the 2nd. boss level.
All of them are time trial levels. You will always have to rush through them. I started them with a friend and we had quite some difficulties in the levels of world 3 and 4 because of the stupid camera system in the game. I recommend doing these in single player. Even though it means you can't be revived by your buddy it's still easier because the camera always focuses on you.
There are perks you can unlock in all of the levels but you do not have to get those. Just play through the 4 levels and the achievement will unlock.
If you need help at any point refer to the videos below.
(you have to fast forward a bit in the videos for world 3&4 since he has some other levels in those as well)
video credit goes to: Dark Adonis
Hope this helps you guys ;-)
Any improvements? Let me know in the comments!