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