https://starbounder.org/Mother_PoptopOn the first planet you arrive at the beginning the game, you'll be able to find a mine you'll need to explore to find 20 Core Fragments to complete the first main quest of the game. You should be able to find this mine just be going left or right on the planet, as the planet seems to loops around on itself.
While exploring this mine, you'll reach a pretty obvious looking arena, surrounded by a couple doors on each side with plant blocks on the ground, you'll find the Mother Poptop enemy in there. She's quite big, an adult form of the little long eared enemies that attack you with said ears. Personally I had found a gun in one of the many crates and boxes you find in the mine, so I just stood above her and took shots at her until she died. I want to say you could always just come back to her later in the game, once you find a gun, if you'd rather not fight her in melee.
Take her out and this will pop.