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