Challenge Mode consists of a series of levels which can be done on all difficulties. The Easy challenge, is, like its name suggests, easy, and has only six levels (Level 6 being Apocalypse). The Medium challenge has seven levels (the seventh being Apocalypse) and Hard is the same way, except harder. The Insane! challenge is the hardest, and has, eight levels, including an easy level at the end called Beyond Apocalypse.
Challenges are great if you are attempting to get DNA, Milestones, and Bones. Don't enable any cheats though, that is if you still want to achieve milestones!