When Wario took over Mario's castle, he sent his six generals to guard each of the 6 Golden Coins to the castle, all of which are needed to enter. Radonkel guarded one in an egg at his nest at the top of the Tree Zone. Mario reached him and fought him. He defeated Radonkel, who was apparently destroyed, and Mario took the golden coin from the egg.
Radonkel swoops down to attack and goes to the opposite side of the screen. He repeats this throughout the whole battle. To defeat him, Mario must jump on him three times. He is perhaps the easiest boss in the game.