From the Super Mario Wiki
Broggy Bonker is a Special Attack used by Bowser in Mario & Luigi: Bowser's Inside Story. When initiated, Bowser will be carrying a filthy Broggy. Then, the player will have to clean Broggy as much as possible by rubbing him with the stylus. The cleaner Broggy is, the more damage the enemy will take. When executed perfectly, Broggy will attack along with the Blitties. This attack costs 20 SP to use, the highest amount in the game for Bowser. It's one of the strongest special attack in the game, while the other is Falling Star, held by Mario and Luigi. Bowser can use this move after finding all 15 Blitties found inside enemies throughout the game and giving them to Broque Monsieur. The Broggy Bonker along with the Shy Guy Squad are the two special attacks not used by Bowser in Broque Madame's minigame.
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