Actually, there's three possibilities for this weapon depending on which path you take...
Trial 2977: Use Any Great Katana weapon skill to deal the finishing blow to 300 experience-yielding members of the Amorph family.
Resulting augments: DMG:+6, Weapon Skill:DMG:+10%
Trial 2978: Use Any Great Katana weapon skill to deal 400 damage or greater to experience-yielding members of the Vermin family 500 times.
Resulting augments: TP Bonus +100
Trial 2979: Use Any Great Katana weapon skill 800 times on members of the Ghosts Family.
Resulting augments: DMG:+6, "Store TP"+12