To Complete This Quest
Talk to the 5 Mercenaries at the beginning of stages 1-3, 1-5, 1-7, 1-9, and 1-10, then beat the bosses of those stages and talk to the mercenaries after to claim your letter.
Take all of these letters to the headmaster of the military academy to the right of the Square to get the Lunia Goddess Necklace.
This necklace is a MUST GET. +5 to every stat, +10 hp/mp, and +30 defense, plus a good reduction in skill cooldown and increase in skill damage = totally worth it !