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