Prep the shrimp. Peel and devein the shrimp, leaving the tails on if desired. Rinse them under cool water, then drain them in a colander, pat dry with paper towels and set aside.
Set up your breading station. Place flour in one shallow bowl. In a second bowl, whisk the eggs. In a third bowl, combine the shredded coconut and breadcrumbs, mixing well.
Bread the shrimp. Working one at a time, dredge each shrimp in the flour, shaking off excess. Dip into the egg, allowing any excess to drip off, then coat thoroughly in the coconut mixture. Gently press the coating onto the shrimp to help it adhere. Place on a plate or baking sheet.
Heat the oil. In a deep skillet or heavy-bottomed pot, heat about 2 inches of oil to 350–375°F.
Fry in batches. Carefully add shrimp to the hot oil without overcrowding the pan. Fry for 2–3 minutes per side, or until golden brown and cooked through.
Drain. Remove shrimp with a slotted spoon and place on a paper towel–lined plate or wire rack to drain.
Serve immediately. Serve hot with sweet chili sauce, lime wedges, or your favorite dipping sauce.