Bake cake batter in two 9x13 pans at 350°F for 22–25 minutes. Cool completely.
Trim cakes to make a tail shape and stack with a thin layer of frosting between. Chill 20 minutes.
Tint half the buttercream teal, a quarter purple, and reserve a little white. Fill piping bags.
Pipe overlapping scallop scales across the tail with the round tip, alternating teal and purple. Smooth edges with an offset spatula.
Melt white chocolate and drizzle for shine. Use the petal tip to add fin ruffles at the tail end.