Before I begin: MAKE SURE YOU SAVE! Achievements have a way to glitch. Saving as a precaution before you're supposed to get the achievement helps you to try again without having to start over.
While it's not considered part of the main story, you will want to right the Hekatonchires if you want to see the rest of the story.
The side quest chain starts with Most Adamantly, which you can start before the main quest ends. The next one you can't start until after it ends.
Anyway, here are the quests in the chain: