Pat the fillets dry. Season with salt and pepper. Place flour in a shallow dish and coat each fillet in flour. Shake off excess flour.
In a large skillet, melt 2 tbsp of butter over medium heat. Place 2 fillets into the skillet. Saute each side until lightly golden, about 1-2 minutes per side. Remove fillets from skillet. Place another 2 tbsp of butter into the skillet and continue with the next 2 fillets.
Reduce heat to medium-low. Add garlic, chili paste, capers, anchovy paste, wine, and salt to the skillet. Stir for about 2 minutes, until the alcohol has evaporated. Add lemon juice and tilapia fillets to the skillet. Garnish with parsley.