Practice performance: There are many NPCs watching both the Valeriano and Brilioth troupes. Certain dances attract certain age groups away from the Valeriano troupe. The goal is to have the biggest audience in the end. Regularly, you will be asked what kind of dance to do: Jigs, which children like, Waltzes, which young men/women like, and Sambas, which older people like. These options come in the form of a menu listed in the following order: Waltz, Samba, Jig. A sixty-second clock accompanies this menu in the upper-left corner of your screen. Quickly select the dance you want to do so you can do more dances within the time limit and garner more favor from the crowd. You may practice as often as you like.
Wait for the Vana'diel day to change, then speak with Laila again for a cutscene where you perform for real.
You must be on DNC to trigger this CS.
Audience is composed of 3 children, 2 young men/women, and 2 older people. Focus on Jigs and Waltzes so at least 5 of 7 will watch your performance and you'll win for sure. If you succeed, you will be rewarded with the Dancer's Casaque.
You must have at least half of the audience (4 people) watching Brilioth to complete this quest.
The actual performance is significantly more difficult than the practice. Even after the clock hits 0:00, there is still about a 5-second window (while the next cutscene is loading) that Valeriano can steal your audience and you are unable to do anything about it.
If the actual performance is failed, you must wait one more game day and zone before you may try again.
Simply alternating Waltzes and Jigs quickly enough guarantees a win. Get to each one as fast as possible (for example, after a Jig, start pressing [Enter] to do a Waltz immediately).