Preheat oven to 375°. In a large skillet, melt 1 tablespoon of the butter over medium. Add onion to skillet and cook, stirring occasionally, until softened, about 4 minutes.
Scrape the onion into a medium bowl and stir in spinach, tuna, feta, dill, eggs, salt, and pepper.
Lay 1 sheet of phyllo on a work surface and lightly brush with some of the melted butter. Lay the buttered phyllo along the bottom of a 9-inch pie dish, pressing to adhere to the dish, and leaving an overhang on all sides. Repeat with 2 more sheets of phyllo and some more of the melted butter. Spoon the spinach mixture evenly over the phyllo in the pie dish. Brush remaining 3 sheets of phyllo lightly with more of the melted butter and scrunch up to ruffle, arrange the three sheets to cover the top of the pie. If there is any remaining melted butter, brush over top of ruffled pie.
Bake until golden and cooked through, tenting with foil halfway through, to prevent top overbrowning, 50 to 55 minutes.