Pumpiron Pengo is the boss of Stonefrost Peak--the fourth adventure.
Clear out the minions every time they spawn and keep your distance from the boss--using the default gun on the boss is effective. I wouldn't suggest melee weapons on the boss because touching the boss damages you and uses heavy attacks when you're near.
This boss has a charge move--standing even at mid-range in front of the boss may activate the charge attack--so distance is really important. Throwing some of the larger objects off the stage will help clear room to effectively kite the boss.
The achievement pops after defeating the boss.