Solve the Three Judges

Beat the Labyrinth without dying or failing

Summon every Soul with the Claws of Hades

Acquire the Boreas Icestorm

Solve Hera's Gardens

Collect all of the Gorgon Eyes

Kill Cronos

Open the Gates of Tisiphone

Successfully entertain Aphrodite

Kill Hercules

Kill Hermes and acquire his Boots

[Phone Trigger] Ignored a phone call.

Cover Kratos in 500 buckets of blood by killing the enemies