After obtaining all of the Titan Tablets, Priest's Amulets, and Emperor's Coins and placing them each in their required pillars a giant stone tablet will appear in the middle of Elysiam. Activate the gaint stone tablet to take you to where you can choose your ultimate weapon challenge.
Annihilation- Beat Axe Challenge 4.
Invictus Gladius-Sword of Vengeance- Beat Sword Challenge 4.
Olympus Cleavers- Beat Gauntlet Challenge 4.