Achievement Name: Nonconformist
Description: You befriended the Goths, like everyone else playing this game.
As the description so humorously points out, this achievement is not missable and will unlock with story progression.
Edit: Apparently it IS possible to waste so much time that it progresses the day before you finish the tasks, but don't ask me how as the entire way this game is set up is done so that it shouldn't progress until you've finished the quest, but just to appease a few people complaining about a solution that is clearly (due to even the description of the achievement) accurate, it may be smart to do these in a timely manner.