Peel shrimp, leaving the tails intact; devein, if desired, and set shrimp aside.
Combine biscuit mix, sugar, and beer, stirring until smooth; set mixture aside.
Coat shrimp with flour; dip into beer mixture, allowing excess to drain. Gently roll coated shrimp in flaked coconut.
Pour vegetable oil to a depth of 3 inches in a large saucepan; heat to 350°. Cook shrimp, a few at a time, 1 to 2 minutes or until golden; drain on paper towels, and serve immediately with Orange-Lime Dip.