You must complete 36 tasks from Hermes's Heroic Tasks Board.
The board is in the Hall of Gods. The requirements count retroactively, so if you've already met the requirements for a task before it becomes active, it will be auto-completed and you can claim the rewards immediately and move on to the next task. If you are trying to 100% the map/vaults you will likely tick off most of these as you play.
If like me you get to the end of the game and have only a handful of Myth Challenges left - you can use this interactive map to quickly find what you missed and where it is. Sadly I don't know who to credit for this wonderful creation, but it's not mine.
https://mapgenie.io/immortals-fenyx-rising/maps/golden-isle**As others have commented, the description of this achievement (at least at the time of writing) appears to be misleading. Essentially you can ignore the word "ALL". Meaning if you've done 35/36 by the end of the game, you could fire up NG+ and pick up one of the easy tasks from the start of the game to complete your 36. I've no idea if this will continue to work though.
If you’re going for the full 1000G you’ll need to do ALL the tasks for the final Phosphor skin anyway, and the vast majority you will have completed passively by just playing the game.
If you'd like to see the 36 tasks up front:Task 1: Defeat 10 animals
Task 2: Defeat 20 Soldiers of the Dead
Task 3: Defeat 40 Mythical Monsters
Task 4: Defeat 3 Lieutenants
Task 5: Defeat 80 enemies
Task 6: Defeat 5 Legendary Monsters
Task 7: Defeat 3 Wraiths in their lairs
Task 8: Defeat 8 Leiutenants
Task 9: Defeat 10 Legendary Monsters
Task 10: Collect all 4 Mythical Fragments by defeating the four Mythical Monster bosses
Task 11: Loot 6 optional chests in the Vaults of Tartaros
Task 12: Complete 6 regular Vaults
Task 13: Complete 2 Arenas in Vaults
Task 14: Complete 3 Hard Vaults
Task 15: Complete all objectives in 22 regular Vaults
Task 16: Collect Molten Fragments from 5 Arena Vaults
Task 17: Complete all Objectives in 10 Hard Vaults of Tartaros
Task 18: Collect all 10 Molten Fragments from Chests in Vaults of Tararos Arenas
Task 19: Collect 6 Ambrosia
Task 20: Tame 1 mount breed
Task 21: Find and Open 9 Normal Chests
Task 22: Open 7 Guarded Chests
Task 23: Collect 25 Ambrosia
Task 24: Find and open 18 Normal Chests
Task 25: Collect 5 Midnight Fragments from Night Chests
Task 26: Tame 2 unique Mount breeds
Task 27: Open 25 Guarded Chests
Task 28: Collect all 10 Midnight Fragments from Night Chests
Task 29: Complete 5 Myth Challenges
Task 30: Complete 3 Fresco Myth Challenges
Task 31: Complete 3 Odysseus Myth Challenges
Task 32: Complete 20 Myth Challenges
Task 33: Complete 4 Navigation Challenges
Task 34: Complete 8 Lyre Challenges
Task 35: Complete 11 Constellation Challenges
Task 36: Complete all 80 Myth Challenges