Must clear the Rocktoise Mob/Mark Hunt mission which given by Pilika in Bhujerba SkyCity. After taking your reward from Pilika, speak to her again and she will tell you there was another matter. Agree to help her would be given a Merchant's Armband, now she wants you to find her diary inside the Clio's Technicks.

Now head to the technick/skill shop, the moogles no longer blocking the stairs to the left. Get close to the bookcase at left corner and take the Pilika's Diary, you're able to choose either Read It or Abstain, but it doesn't matter for now, however, if you choose Read It, you can spot a mini serpent on top of the other bookcase looking at you (Easter Egg?).

When you return the diary to Pilika, she will ask whether you had read the diary, now your answer affects the reward. It's either level 2 or level 3 Mystic Armor.

Lv2 - Kilimweave Shirt, awarded if you say you read it.
Lv3 - Shepherd's Balero, awarded if you say "I've done nothing"