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