Dead Age

This achievement is unmissable and will unlock at the start of Day 20. However, there is one required mission that needs to be completed to be able to reach this point (unlike most other missions which can be skipped/ignored):

On Day 10, a mission called "The Radio Tower" will appear. This is a two part quest that needs to be done by Day 14 or you will get one of the bad endings of the game. This quest will require you to gather a certain amount of Tools and Materials. Of the two needs, you should definitely have enough Tools at this point -- if you're doing all the missions in the game up to this point, you should have plenty of Tools saved up already. If not, complete another quest on Day 10 or head to the Woods Night to collect some. As for Materials, sell some Gold, Gas, Bullet Casings, Old Weapon Parts, Old Clothing, Engineering Parts, etc until you get enough -- Materials should be the easier of the two needs to "fix" unless you've been selling and spending like crazy; if short, just collect stuff while out collecting Tools, and sell it to the merchant to get enough Materials. Once you reach the required amount of Tools and Materials, both should immediately be removed from your inventory and part two of "The Radio Tower" will commence.

Part two of "The Radio Tower" requires you to go through Highway Night to Area 10, whereupon you'll automatically fix the radio tower, completing the quest and automatically returning you to camp. This needs to be done by Day 15 or the game will reach on of its "Bad endings", preventing you from reaching Day 20.

Once this quest is done, play as per normal and the quest will unlock at the beginning of Day 20.