This is the idea:
Every time you clear 3 waves of any stage without sweep tickets, there's a chance that you might find a bonus boss which will scale in difficulty according to which chapter it is. The rare bonus boss once killed, will drop the items/fragments of the stage cleared plus extra bonus goodies.
Goodies
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Stamina
Gold
Gems
Sweep Tickets
Gold Chest Tickets
(Very rare) Diamond Chest Ticket