Return to Luca during Chapter 1 before visiting the Zanarkand Ruins to complete a side mission explaining where Yuna was during her impersonators performance.
Moogle Mission
After arrival, you will be in control of Yuna wearing a Moogle costume. She will be on a side mission to hand out 10 balloons. She can sell them to every NPC in the plaza area except for a little girl running around and a man in green (there are some hidden people behind the glass window and at the back of the red carpet at the door to the cafe). After completing this task, you will be awarded the Healing Wind Garment Grid.
Learning Sphere Break
After the Moogle mission is completed, return again to Luca for more items and learn about Sphere Break. Upon arrival, descend the stairs and jump up and across to the pathway ledge for a chest containing Lunar Curtain x2. Head all the way down the stairs and then across the plaza. Follow the path to the left until you reach the stadium. Head up the stairs to the right locker room hallway. Here you will find Rin. Talk to him and he will explain how he created a popular game called Sphere Break. After speaking with him, head out back to the front of the Stadium, this time go to the left locker room hallway. Speak to the little man wearing a beak. Ask him to "Tell me the rules!". He will go through a tutorial of the game and then award you Helm Coin x5, Zurvan Coin x5, Coyote Coin x5, and Flan Coin x5. Exit the locker room and from the receptionist desk, head right to Dock 3. Walk all the way to the back left-hand side. You'll see an entry way to behind the stacks of cargo. Walk through it and, you'll see a chest. Open it to obtain the Thunder Spawn Garment Grid. Head back to the airship or on to Mi'ihen Highroad when finished and continue on in the story.