In a medium saucepan, combine 6 cups of water with the salt and sugar. Bring the mixture to a rolling boil over medium-high heat.
Prepare a large bowl filled with ice water and place it near the sink for immediate use.
Carefully add the shrimp to the boiling water and allow them to cook for precisely 3½ minutes, or until they turn pink and opaque. It's normal if the water doesn’t return to a full boil after adding the shrimp.
Once cooked, drain the shrimp in a colander, then quickly transfer them to the ice water to stop the cooking. Let the shrimp cool for around 15 minutes.
Meanwhile, prepare the cocktail sauce by mixing the ketchup, horseradish, lemon juice, lemon zest, Worcestershire sauce, and hot sauce in a small bowl. Adjust the seasoning to your taste preference.
Peel the shrimp, leaving only the tails intact. Arrange the shrimp on a platter over crushed ice, if desired, and serve alongside the cocktail sauce. Enjoy!