Here is the full list of all 31 Apotheon trophies - there are 8 bronze, 18 silver, 4 gold and 1 platinum.
Acquire the powers from all twelve Olympian Gods
Acquire the Thunderbolt of Zeus
Find all lockboxes on Olympus
Find all rare weapons on Olympus
Access the Gold Mine in the Sea
Acquire the Trident of Poseidon
Access the sunken wreck of the Euphemia in the Sea
Aquire the Sandals of Hermes
Aquire the Kantharos of Dionysus
Aquire the Cestus of Aphrodite
Access the Refugee stash in the Forest
Access the Assassin Stash in the Swamps
Access the Agora Market Scroll-keeper’s Office
Access the Agora Armoury
Root out the assassins in the Acropolis
Acquire the Crest of Ares
Acquire the Aegis of Athena
Access the Merchant Stockpile in the Acropolis
Access Kleio's gift in the Acropolis
Aquire the Artifice of Hephaestus
Acquire the Lyre of Apollo
Access Apollo's nectar cellar
Access the Symposium of the Sun in Apollo's hall
Meet the Necromancer in Hades
Access the Secret Grove at the Shrine of the Nymphs
Acquire the Bow of Artemis
Access the Hunter's Trove in the Forest
Acquire the Sheaf of Demeter
Ascend to Mount Olympus
Unlock all other Trophies
Beat game on Olympian Difficulty