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