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