The Festival of the Hunt occurs during your first visit to Lindblum.
In order to have Vivi win, both Freya and Zidane must forfeit by dying. To get this to happen be in the Business District and go to the Square after the counter gets down to 4:30 or less. A Zaghnol will have spawned and they will fight together under your control. Simply have them both attack themselves until they die and Vivi will the hunt netting you this trophy during the following scene.