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