Destroy all the green polyps inside Paul in 'Pop His Top'.

This achievement is the trickiest in the DLC adn is done in the 4th mission, 'Pop His Top'. The polyps are the large green balls floating in Paul. Not the small object. There are a lot of polyps you have to hit and you have a cool down on your weapons so shoot sparingly until you get to the hallways where there are a lot of polyps, when you reach this point just unload. If you are playing in co-op, the second player shoots. Solo or co-op it is good utilize the ship and crash into any polyps you are about to miss. Both being shot and rammed into count as destroyed. If any polyps are missed, you must restart the entire level. Reloading the checkpoint will null the achievement.

And shouldn't they be called PAUL-yps?

Here is a video demonstration of how to get the achievement