Bring a large pot of salted water to a boil (about 1 tablespoon salt for 4 quarts of water). Add 1 pound medium shells pasta and cook according to package directions. Drain and rinse with cold water until the pasta is cooled.
In a large mixing bowl, combine the cooked pasta, 3 (5 ounce cans) solid white albacore tuna (drained), 1/2 cup minced red onion, 4 medium celery ribs (diced), and 1 cup frozen peas (thawed).
In a separate small mixing bowl, whisk together 1 cup mayonnaise, 1/4 cup lemon juice, 1/4 cup minced fresh dill, 1 to 2 tablespoons granulated sugar, 1 tablespoon Dijon mustard, 1 teaspoon salt, and 1/2 teaspoon black pepper until well combined.
Pour the sauce over the pasta and stir until everything is well coated.
Cover the bowl with plastic wrap and chill for at least 1 hour before serving.