Boomer Mech is the boss of Giant World in Parasol Stars. Mecha mighta. In Bubble Bobble and Bubble Symphony, mightas are the guys who look like ghosts and fire boulders at you. This mechanical mighta throws boomerangs.
Immediately go snag the Star Bottle, followed by dropping to the floor and running right underneath the Giant Mech. Now Charge up the Star Droplet, releasing it on the opposite side of the room from his boomerang attack (this attack covers one half of the room), followed by running through to the side that was just attacked, repeating the procedure, this time on the opposite side of the room (five hits will take him out). The other method involves getting up to a ledge on level with the Giant Mech, followed by rapid firing 15 droplets into the mechanical monstrosity, but be wary of leaving a small opening as a boomerang can come flying out to kill Bubby or Bobby. Grab the treasures that are the spoils of victory, moving on to the next planet soon after.