This achievement requires you to acquire all 120 friends in the game, INCLUDING Clyde at the very beginning of the game, who is technically the 121st friend, but he removes you immediately after being banished. You must talk to Clyde right in the beginning of the game in Kupa Keep, before talking to Cartman, or you'll be unable to unlock this achievement even if you get all 120 friends.
Follow the Friends guide Here for a rough chronological list of all 121 friends. It also highlights which friends are missable. Also use the Missable Guide, which includes missable friends in each quest when they appear.
Keep in mind that while there is no New Game+ to get missable friends, there is post-game play where you can mop up some friends that you may have missed while playing (the un-missable friends), so if you aren't complete with the friends list by the time you finish the game, as long as you've gotten the missable friends, you can go back post-game and get the remaining ones to unlock this achievement.