Escalation Battles are a type of Special Stage. These stages have a level that increases, along with the catchability, which is equal to the level, and also the stage difficulty, each time the player clears the stage. The catchability does not receive a bonus from remaining moves or time. Rewards are given out for clearing certain milestone levels, usually in increasing rarity. These stages are infamous for giving out lots of Mega Speedups and other Enhancements.
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