By meeting arbitrary conditions within the game, you will achieve the accolades designated in the Challenges menu.

Challenge	How to unlock
A trip to the sky	Reach level 3.
A walk in the forest	Reach level 2.
An epic secret	Find the secret item.
An unexpected twist	Unlock Sparky Child.
Books also exist	Play the game for more than five cumulative hours.
Can I play with ... time?	Unlock Chronos Twins' Nec.
Crazy jumper	Jump more than 12,345 times.
Golden Cubit Invocator	Collect every "Impossible" item.
Guru of the equilibrium	Finish level 5.
Hardcore Lord	Complete every one of the other 23 Challenges.
Highly extroverted	Crash into enemies more than 250 times.
I love zig-zags	Reach level 5.
Lord of the skies	Finish the final level.
Master of the (hard)core	Finish level 4.
My first date	Unlock the Cubit Girl.
My first star	Collect your first "Impossible" item.
No longer a rookie	Achieve a high score greater than 500,000 points.
Reaching the core	Reach level 4.
Running through the sky	Reach level 6.
Seriously?	Play more than 1,500 games.
The closer	Finish every level.
The living dead	Die more than 1,000 times.
The void explorer	Fall into the void more than 250 times.
Thief of the sky	Pick up a star 3 times in a single game.