You can acquire Special Fragments by playing levels that serve as upgrade material. 

With Special Fragments you can create a character from a list which is updated daily.

Please keep in mind that completing one event doesn't automatically mean you can create a character. 50 Fragments are required to do so, and the maximum number of Fragments you can get in one event is 39. But you do have the option of obtaining Special Fragments in the Market.

This kind of event has a special mechanic which allows you to revive and continue from where you left off.