To win the Flower Trophy and beat all the competition in your town, plant a bunch of Purple and Black colored flowers. These flowers are very rare and Tom Nook doesn't sell them. To find them, walk around your town and look for them growing. They grow randomly only once a week. When you find one, pick it and put it in your dresser. When it's time for the Flower Fest, take the collection and make your entire garden out of them. With this garden, you will win the contest and receive the Flower Trophy.
To win the Flower Trophy , take all of the flowers form your neighbor's gardens during the Flower Festival and plant them around your own house.