Here is the full list of all 31 Tethered achievements.
Complete the tutorial level
Build a Temple
Upgrade a building
Build a Moot Hall
Upgrade a resource
Build a Barracks
Complete level 5
Complete level 9
Complete level 13
Bring Harmony to all Islands
Build a Workshop
Sacrifice 10 martyrs across any levels
Have seven heroes active on one level
Kill 100 critters
Build at least one of every building and upgrade across any number of levels
Rate A in all categories on a level
Have only a single injured hero peep left alive at the end of a level
Rate A in all categories across all levels
Survive five nights on a level
Have at least one of each craftsman during the course of a level
Use each type of weather at least once
Fill your tavern during the night
Hatch 100 eggs across any number of levels
Kill 20 critters with a watchtower across any number of levels
Earn 500 SE from Sacred Altars across any number of levels
Unleash a frankenpeep and use it to kill 5 critters
Burn a holy beacon for an entire night
Have five peeps with clogs on during a level
Kill ten critters with grenades
Store a rainbow in a cloudbuster
Upgrade a hero with clogs, armour and sharp tools