Heat a large skillet over medium-high heat. Add 1 tablespoon oil. Add tilapia fillets, salt, and pepper and cook until easily flaked with a fork, about 2 minutes on each side. Turn off the heat and shred the fish with 2 forks. Transfer to a bowl.
Toss the fish with bread crumbs, green onions, egg, lemon juice, feta cheese, garlic powder, dill, and hot sauce.
Form patties with your hand and refrigerate for at least 1 hour.
Set a skillet over medium-high heat. Add remaining oil. Cook patties in the hot oil until golden brown, 1 to 2 minutes on each side.