Pat the tilapia fillets bone-dry with paper towels. In a small bowl, combine smoked paprika, garlic powder, ginger, salt, and pepper. Dust both sides of the fish evenly.
Heat avocado oil in a 12-inch skillet over medium-high heat until shimmering. Sear the fillets for 3-4 minutes per side until a mahogany crust forms and the fish flakes easily. Remove fish from the pan and set aside on a plate.
Lower the heat to medium. In the same pan, add the melted coconut oil and minced garlic. Sauté for 30 seconds until fragrant.
Pour in the coconut milk and brown sugar, whisking constantly. Let the sauce simmer and bubble for 3-5 minutes until it thickens slightly.
Remove the pan from the heat and stir in the fresh lime juice.
Return the seared tilapia to the pan, spooning the coconut sauce over the fillets. Garnish with shredded coconut.