Here is the full list of all 52 Soul Axiom trophies - there are 42 bronze, 7 silver, 2 gold and 1 platinum.
Collect all Soul Axiom trophies.
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Complete all three endings
Complete Doctor's Ending
Complete the Volcano
Defeat the Volcano Angel without any Deaths
Find all the Monkeys
Complete Dana's Ending
Complete Solomon's Ending
Complete the Office
Complete the Waiting Room
Complete the HUB
Complete the Corrupt Winter HQ with No Deaths
Visit the Prehistoric Era
Beat the Crows without dying on the Corrupt Mansion
Complete the Tree of Life
Find Seren in the Tree of Life
Complete the Forest
Find the Corrupt Power
Complete the Winter HQ
Find all the Eyes
Complete the Apartment
Complete the Church
Complete the Space Station
Find half the Monkeys
Complete the Mansion
Complete the University
Find the blue duck
Complete the Hospital
Find the "kids" Owl picture in the Hospital
Complete the Ice Palace
Complete the Clock Puzzle without dying in the Ice Palace
Find the Destroy Power
Complete the Museum
Trigger the shark attack on the Museum
Find half the Eyes
Complete the Beach
Trigger the shark attack on the beach
Complete the Warzone
Complete the Jungle
Destroy the Right Monkey in the Jungle
Find the Play Power
Find the first Monkey
Complete the Monorail
Complete the Puzzle on the Monorail
Complete the Elysian Fields
Complete the Desert Temple
Phase the Ball in the Desert Temple
Find the Phase Power
Complete the Desert
Complete the Ship
Find the first Eye