To unlock this Achievement you must progress to:
This is best done on "I'm too young to die" Difficulty, as there are no unlocks for any difficulties above this from the campaign (Except completing "The UAC" on Ultra-Nightmare).
To defeat the boss, make sure to keep your distance from its attacks and use heavy weapons such as the BFG, Gauss Cannon, or Chaingun, preferably with fully upgraded mods (eg Siege Mode for the Gauss Cannon). Make sure to jump on top of the pillars which are spawned when it performs a purple AOE attack (don't shoot them or they'll break!), and use this time to get precision hits on the weak point (the big bulbous head). The BFG stuns it on hit, which can be used in conjunction with another weapon to deal damage to it while it is immobile from the BFG effect. Continue to deal damage until the Glory Kill opportunity triggers.
This battle is best described by the first Boss' Achievement title: Shoot it until it dies.
PowerPyx's cover of the Boss Battle: