Challenge Times are special level completion times that the developers put in for each level. They are hard to beat, but give you Coins Galore stages. To unlock the Challenge Times, simply collect all gems and complete all Bonus Challenges in an episode.
After doing all three episodes of the main game and completing every stage, finding every gem, and doing every extra challenges the levels offer, the bonus book pages become available. After 100%ing those, Mummy Me Maze Forever becomes available. Get to the 50th floor on that and you unlock a crown for Captain Toad to wear in any level.
If you have a save file on your Wii U of Super Mario 3d World, a bonus option should show up for you on the main screen. This allows you to explore certain levels from Super Mario 3d World as Captain Toad!
Leave the game on the title screen for 30 seconds and it will load either a fountain level or a gallery level. Walk up to the blue toad for a mushroom worth 10 coins.
In order to unlock the secret levels in the bonus book, you must complete the book that the level is in.Ex. Complete book 1 = prologue level 1
On the Episode books, you can have a maximum of 3 Toad Stamps on the front cover of each book. To get the first stamp, complete the episode. To get the second stamp, collect all of the gems in each level of the episode. To get the third and final stamp, collect all of the gems and complete all of the Bonus Challenges in the episode. To obtain little glittering stars around the stamps, beat all of the Challenge Times. Finding the Pixel Toad on every level within an episode book will also adorn the cover with a golden Pixel Toad.