Here is the full list of all 39 Inkbound achievements.
Master 100 Vestiges.
Reach level 100.
Free the Captive.
Master 50 Vestiges.
Find the Gatekeeper and OHM.
Collect the "Magic Threads".
Reach level 50.
Win a run with 1,000 or more Kwillings.
Find the Opal Slab.
Unlock all Trinkets.
Unmask the Unbound.
Reach level 25.
Reach level 10.
Heal another player.
Win a group run.
Start a group run.
Win a Solo Run at Challenge Rank 10.
Die for for the first time.
Unlock a Trinket.
Defeat a Villain for the first time.
Equip enough Vestiges to fill your inventory.
Fully upgrade a Binding.
Enter the Atheneum for the first time.
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.
Master all Vestiges.
Defeat the Villain in a Daily Challenge.