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