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