Here is the full list of all 31 Tethered achievements.
Complete level 13
Bring Harmony to all Islands
Complete level 9
Hatch 100 eggs across any number of levels
Complete level 5
Burn a holy beacon for an entire night
Build a Temple
Kill 100 critters
Survive five nights on a level
Complete the tutorial level
Build a Workshop
Use each type of weather at least once
Upgrade a building
Build a Moot Hall
Upgrade a resource
Build a Barracks
Sacrifice 10 martyrs across any levels
Have seven heroes active on one level
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
Have at least one of each craftsman during the course of a level
Fill your tavern during the night
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
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