Here is the full list of all 39 Inkbound achievements.
Reach level 10.
Win a group run.
Heal another player.
Start a group run.
Complete all Aspect Quests.
Win a run without acquiring any augments.
Win a run without drafting any bindings.
Win a run with 1,000 or more Kwillings.
Defeat a Villain without defeating any other unit in that fight.
Unlock a Trinket.
Die for for the first time.
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.
Free the Captive.
Collect the "Magic Threads".
Find the Gatekeeper and OHM.
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 vestiges.
Win a run without taking any damage.
Win a run without collecting an Orb.
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.