Light your fire, then Upgrade the Camp As Soon As Possible.
- There is a hidden cooldown before you can upgrade it after lighting the fire.
To get "Free Walls" you need to upgrade it a second time before "The Second Day" ends.
It ends as the Day III graphic pops on the screen.
If you Upgraded the camp as soon as you could, you should be able to upgrade to "free walls" level as the moon is setting on your second day.
GL!
P.S. Skip the Tutorial (makes you build a wall)
Do not build any walls before the achievement pops just to be safe ;D