Here is the full list of all 39 Inkbound achievements.
Free the Captive.
Master 100 Vestiges.
Find the Gatekeeper and OHM.
Collect the "Magic Threads".
Reach level 100.
Master 50 Vestiges.
Find the Opal Slab.
Unmask the Unbound.
Reach level 50.
Unlock all Trinkets.
Reach level 25.
Defeat the Villain in a Daily Challenge.
Reach level 10.
Win a Group Run at Group Challenge Rank 10.
Win a Solo Run at Season Challenge Rank 20.
Win a Solo Run at Challenge Rank 10.
Win a run with 1,000 or more Kwillings.
Unlock a Trinket.
Win a run without taking any damage.
Defeat a Villain for the first time.
Win a group run.
Fully upgrade a Binding.
Die for for the first time.
Heal another player.
Equip enough Vestiges to fill your inventory.
Start a group run.
Enter the Atheneum for the first time.
Win a Group Run at Group Season Challenge Rank 20.
Win a run without ever moving in combat.
Complete all objectives in the Victory Board.
Win a run without acquiring any augments.
Win a run without acquiring any vestiges.
Defeat a Villain without defeating any other unit in that fight.
Win a run without drafting any bindings.
Win a run without collecting an Orb.
Complete all Aspect Quests.
Master all Vestiges.