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