Collect all 160 fragments before claiming the Chaos Crystal weapon at the front counter in Academia 4XX AF. With all 160 fragments, the weapon will be in its strongest form. Note: The Chaos Crystal can be purchased in Serendipity for 10,000 coins (7,500 with the Haggle skill). Give the Chaos Crystal to Hope in Academia 4XX AF and he will tell you to claim the weapon at the front counter. It does not matter which one you choose, because the other weapon can be purchased in Serendipity for 1,000 coins (750 with the Haggle skill) after claiming the first weapon.