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