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