For every Special Chapter cleared, you will receive a Stage Clear Reward.

However, in addition to simply clearing the Stages, different missions may be given depending on the types of different Special Chapters.
Therefore, the mission-specific requirements for receiving rewards and the types of Special Chapters may vary.

Special Chapter types and clear requirements
Normal type: Clear all the Stages in the Special Chapter.
Collection type: Clear all the Stages in the Special Chapter and collect certain objects.
Score collection type: Clear all the Stages in the Special Chapter and obtain objects by clearing higher than the targeted score on each Stage.