Defeat the Worm Boss without defeating any Small Worm.
This boss is weak against Fire Damage. You can solo him starting around Level 10, but if you want to do this trophy quickly and burn him down, it’s recommended you wait until you reach Level 30.
To start the fight, you need to hit the worm tail that is sticking out of the ground.
Once it starts, there are two parts of this boss that repeat until he is down. There are a few differences in the fight if you’re doing it solo versus with multiple people. The first being his HP is higher and the second being tied to Part 2 (listed below).
Part 1: You cannot attack him on this part (he’s immune to everything). He will shoot large green gaseous orbs at a random player. They are slow moving, so as long as you keep running, you can easily avoid them. If you are playing with multiple people, just make sure no one is running too close behind another person (keep your distance from each other).
Part 2: After he shoots the second orb, he will spaz out in the middle and Small Worms will appear on the level. Do not hit these! Included with these will be one or more worm tails. They’re bigger than the small worms and are identical to the tail you hit to start the fight. If you’re playing solo, only one will appear, but if you’re playing with multiple people, two will appear. When you get close to them, their name bar will show "Worm Tail". Hit all the tails that appear and the Boss will fall to the ground, making him vulnerable to attacks. Note: There is a chance he will glitch out and no tails will spawn right away. Just keep going and he'll eventually spawn them (this can be seen in the Warrior run in the video below).
He’ll get back up after a short time so rinse and repeat the fight until his health is fully depleted. If you got him down without hitting any small worms, the trophy will unlock. If you managed to do this on your first encounter with him, Exterminator will also unlock.
If you make a mistake, you can reset the boss (and the fight) by having all players go back down to the Landing Pad (either run or teleport through the map).
If doing this at Level 30, the Talents/Specs used for each class can be found in this post.
Below is a video showing this fight solo with all three classes, and one run on co-op, just in case you need more help.
Note: The Ranger in the video is level 28 with level 22 crafted gear. The Mage and the Warrior are both level 30 with level 26 crafted gear. Everything they're using/wearing can be crafted at the Workbench (Ranger), Altar (Mage), and Anvil (Warrior). This is by far not the best gear available in the game.