To get this achievement you need to finish the game and defeat the punk boss. You have to reach the bunker by day 42 to successfully complete the game, and you need to have finished the quest to kill the punk boss before then to get this achievement. The quest appears a couple days before day 42 and requires going all the way through the desert to area 20 and beating the boss.
To get the best ending (successful ending 3, which also has an achievement) you need to defeat the punk boss AND get the secret weapon, which requires taking Mason with you and getting to the end of the desert, after reaching the bunker for the last quest, as well as fighting a boss. You can get this and the best ending on the same playthrough if you beat the punk boss and get the secret weapon, so make sure you do so. Then the rest of your playthroughs only need to be bare minimum effort playthroughs to win.
Since the quest and the end of the game are so close together, try to conserve medical supplies so you can get into the last quest of the game with 6 medkits. I only had a few and it was a little rough. The good news is when you reach the bunker in area 15 everyone is healed, so the final push is pretty easy, it's just getting there when you just made it to area 20 of the desert a few days ago that can pose a problem.