The Atlantis Quests have item requirements which are not available for purchase in the town. Instead you must defeat monsters to collect them as loot. All of the Atlantis Quest items can be collected off Serpents. This is your best bet for getting the required items. But the items can drop as loot off other battles.
Below is a list the items required, how many are required, and confirmed places to get the items.
Atlantean Archer: 15 – Serpents;
Spartan Warrior: 20 – Serpents; Battle of the Dark Legion; Deathrune Campaign Raid; Genesis, the Earth Elemental
Spartan Helm: 20 – Serpents; Kull, The Orc Captain; New Player Reward
Spartan Sheild: 20 – Serpents; Battle of the Dark Legion; Deathrune Campaign Raid
Spartan Spear: 20 – Serpents; New Player Reward