Here is the full list of all 16 ITTA achievements.
Defeat All Bosses Without Dying
Complete ITTA
Kill Mono Only Using The Revolver
Collect All Spirit Cats
Complete The Shepherd's Story
Collect All Spirit Weapons
Receive Inner Beast's Spirit Blast
Complete The Architect's Story
Collect All Heart Upgrades
100% Map Completion
Open The Void Gate
Enter The Yorke Ruins
Receive Inner Beast's Homing Spirits
Enter The Glass Garden
Keep Itta's Dying Mother Company For 1 Minute After Talking
Receive Inner Beast's Fire