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