When you complete the game and then load your cleared saved game file the question mark that previously appeared on the lower right corner will be replaced with the 'Time Trial' option. There are 5 extra levels (one from each World) in Time Trial mode that are playable with a black Yoshi.
For starters, this challenge is unlocked in the 1st world 2nd level. It involves you to jump of a platform and 'flutter jump' (pressing B and holding) as far as you can go. It isn't hard to get over 130 on this challenge if you have the right technique. Begin by pressing and holding the Y button.(This makes you run giving you a boost) Go to the very back wall and run and jump of the platform. Hold B until the jump wears out then quickly press and hold B again. Keep on doing this until you hit the ground. If you do this correctly you should get about 100-150 meters on this challenge.