In order to unlock this achievement your top priority should be cutting down all the trees you can every day.
On Day 1 you need to set up your defenses to survive long enough to clear an acre of land: build a camp, hire the two beggars, buy 2 bows, run to the right until the first camp, and hire 1-2 beggars. Return to the camp, wait for your archers to get enough coins to buy a hammer, build wooden barricades on both sides of your camp. Survive the night.
On Day 2 start marking all the trees you can for your builder to cut down, both on the left and on the right side. Use the coins from the chest and from your archers to hire more beggars and buy 1-2 hammers to speed the things up. Spend the rest on getting some more archers. They not only will protect your camp, but also be your main source of daily income. Though it is not essential to get a lot of archers for this achievement, you will need plenty to be able to defend your camp during the Blood Moon, if you don't manage to unlock the achievement by then.
Repeat the same process every day, and eventually this achievement should unlock. If your builders are getting caught by the Greed, don't forget to buy more hammers to be able to keep cutting down the trees.
I was able to unlock this achievement on Day 5.