From the Super Mario Wiki
A Mini Battle is a battle with a Bandit in Super Mario World 2: Yoshi's Island and its remake Yoshi's Island: Super Mario Advance 3. A Yoshi will fight a Bandit in one of four battles, either Throwing Balloons, Popping Balloons, Watermelon Seed Spitting Contest, and Gather Coins. They are fought in certain levels after a Yoshi gets a key to the Bonus Game shack. Later, they can be played on the level selection screen.
If the player does so, a screen will pop up listing all the Mini Battles, along with a 2-player version (removed in Super Mario Advance 3) of Watermelon Seed Spitting Contest and a 4-button Throwing Balloons mode. In single-player, Throwing Balloons can either be played so that a 4-button or 6-button combination (indicated by the icon) is required to throw the balloon.
In Yoshi's New Island, the Ground-Pound Pop minigame was based on the Popping Balloons Mini Battle.