Luca
There’s nothing to do in Luca except participate in the Sphere Break tournament. There are a few cutscenes that take place as you enter Luca, and Shinra will mention that the reward for winning the Sphere Break tournament is a Dressphere, so you’ll want to win it.
Sphere Break Tournament Qualification
The goal here is to win three games of Sphere Break. Save your game after the second win: the third victory sends you straight into the final against Shinra, the final challenger, with no save in between. Once you beat him, you’ll win the tournament and earn the Dressphere.
There are two routes you can use to learn more about Sphere Break. You can use the video tutorial below or head to the Sphere Break section of the guide using the link below:
A video demonstration of how Sphere Break works and how to win consistently.
Helpful Hint
Note that you can win a 
Treasure Hunt Garment Grid as long as you make a combination using a border coin that has the “Item” or “Rare Item” trait. It’s not the end of the world if you miss it, but Treasure Hunt grants 
Mug, which lets regular attacks steal items as they hit.
The same trick also works on another opponent. Challenge the woman with the dog, land an “Item” or “Rare Item” combo, and you can win the White Signet Garment Grid.
Side Quests
This section of the guide provides a full overview of Sphere Break, the different rules that you need to know about, and a calculator you can use to help you play it if you’re struggling.
Defeating Shinra will net you the Lady Luck Dressphere. Lady Luck is a great Dressphere, even if it doesn’t seem like it at first. Check out the Dressphere write-up below:
Dresspheres
Relying on getting lucky with dice rolls and critical hits, the Lady Luck Dressphere is a glass cannon that can deal incredibly serious damage to enemies that are otherwise immune.
Helpful Hint
One of the most important abilities that the Lady Luck Dressphere comes with is the 
Double EXP ability. This helpful ability doubles the experience points of the character wearing the Dressphere. Still, you can rotate Yuna, Rikku, and Paine through their Lady Luck Dressphere to help level them up even more quickly. This guide will include additional reminders, but it’s worth setting up each character’s Dressphere abilities page so that they start learning Double EXP as quickly as possible.
The last thing to do, before you leave Luca, is complete the Publicity and Marriage Campaign steps:
Side Quests
A list of the NPCs that you can speak with to earn Open Air / Argent Publicity points and Marriage matchmaking points in Luca during Chapter 3.
And with that, it’s off to the next location. You can actually walk back up to the outer limits of town and climb the stairs to reach the Mi’ihen Highroad (or warp there if it’s faster).
Checking the “Luca Complete” box adds the Story Completion Percent for the automatic scenes in Luca.