Make tartar sauce. Chop hard boiled egg and pickles. Mix them with mayonnaise, and season with salt and pepper. Refrigerate until using.
Peel shrimp shells leaving tails. Make small diagonal cuts on the inner side of each shrimp and pull to help straighten. Sprinkle salt and pepper on both sides of the meat.
Coat the meat with flour, dip in the beaten egg, then cover with bread crumbs.
Heat deep frying oil to 350 F, and deep fry the crumb-covered meat. You can check the temperature by dropping a bread crumb in the hot oil. If it comes up to the oil surface right after it's dropped, it's good.
Fry the shrimp until the color of the coating turns golden brown and the shrimp floats in the oil, about 4-5 minutes, turning a couple of times.
Serve shrimps on a plate with tartar sauce.