On Disc One, not long after arriving in Lindblum, the Festival of the Hunt will begin. The objective is to kill monsters released in to the city to earn points. Earn the most points and you win. There are three possible outcomes; Zidane wins, Freya wins, or Vivi wins. To earn this achievement, Vivi must win the Festival of the Hunt.
In order for Vivi to win, both Zidane and Freya must be defeated in battle. Don't worry, during the Festival this doesn't count as a game over. In order to do this, you must wait until there is under 5 minutes on the clock, and go to the Square in the Business District. There is an item shop, weapon shop, and synthesis shop in the area. Here you will see the Zaghnol threatening two children. Zidane and Freya will team together for the fight. Have Freya and Zidane attack Freya until she is KO'd, then have Zidane attack himself. Once both are KO'd, a message will appear that Zidane and Freya have been retired. A scene will then play in the castle where Vivi receives the award for winning the Festival. The achievement should pop here.