Mouser was the boss of the first world, encountered at the end of 1-3. He attacked by throwing bombs, but Mario, Luigi, Peach, and Toad picked up the bombs and threw them back at him. When the bombs exploded, he took damage. After three hits, he was destroyed.
Another Mouser, a different colored one, was the boss of World 3-3, and was fought the same way, but took five hits instead of three. There was also a Spark in his battle arena that destroying it would make the battle easier.