Here is the full list of all 9 The Companion achievements.
Interact with 15 Runic Stones.
Interact with 90 Runic Stones.
Act I: Witness the children swimming.
Act II: Witness the Father checking if anyone is home.
Act III: Vanquish a creature from within the nightmare.
Act IV: Witness the family resting during their travels.
Act V: End it.
Prologue Part II: The Family sees you.
Visit the top of the Falls