You need to destroy a portal by Day 10. I'm not sure if destroying it on Day 10 will count.
Your highest priority should be upgrading the camp as soon as possible in order to be able to hire a knight and attack a portal.
Build the camp, hire an archer and a builder, build wooden barricades on both sides of your camp.
Run left/right to discover the location of the wooden shrine. If you find a treasure chest on the way and have enough coins, you can upgrade it now. If not, be sure to return and upgrade it later (preferably before Day 4).
Cut down the trees to get enough space for your archers to hunt.
By Day 4 or Day 5 you should have a fully upgraded camp, a second wooden wall in the direction you plan to attack, a knight and enough archers to defend the camp (at least 2-3 on each side).
On the day after the Blood Moon send your knight to attack (you need 4 coins to order an attack).
Repeat the same process at the start of each subsequent day until you destroy the portal and unlock this achievement (remember to re-hire the knight and have enough archers at all times).