Pat the shrimp dry on both sides and season them with salt and lime zest. Keep them in the fridge until needed.
To make the beer batter, mix all of the dry ingredients together in a bowl until they're well combined.
Slowly pour the beer into the dry ingredients, stirring with a whisk or chopsticks until the batter just comes together. It should be thinner than pancake batter but thicker than crêpe batter (about the consistency of heavy cream). It will have some lumps. Don't overmix it.
Heat 1 inch of oil and a frying pan to 350°F.
Once the oil is hot, dip the shrimp piece by piece into the batter one by one, letting the excess batter drip off. Fry them in the hot oil. Use tongs to turn them for even frying. Fry them in small batches so they don't get crowded.
Fry the shrimp until they turn golden brown and reach an internal temperature of 145°F, about 2 to 3 minutes total. Once they're done, transfer them to a wire rack or a paper towel-lined tray to drain.
Sprinkle them with a bit of salt and serve hot.