Here is the full list of all 39 Inkbound achievements.
Win a run without acquiring any augments.
Win a run without collecting an Orb.
Reach level 10.
Defeat the Villain in a Daily Challenge.
Collect the "Magic Threads".
Complete all objectives in the Victory Board.
Win a group run.
Heal another player.
Start a group run.
Defeat a Villain without defeating any other unit in that fight.
Win a run with 1,000 or more Kwillings.
Free the Captive.
Win a run without taking any damage.
Win a run without ever moving in combat.
Win a Solo Run at Season Challenge Rank 20.
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 acquiring any vestiges.
Win a run without drafting any bindings.
Complete all Aspect Quests.
Find the Gatekeeper and OHM.
Reach level 25.
Reach level 50.
Reach level 100.
Unlock all Trinkets.
Master 50 Vestiges.
Master 100 Vestiges.
Master all Vestiges.