Fill a large pot with water, add a generous pinch of salt, and bring it to a rolling boil. While waiting, prepare an ice bath by filling a bowl with cold water and ice.
Once boiling, add the shrimp in a single layer, and cook for 2-3 minutes until they turn opaque, pink, and firm to the touch. The water should bubble gently around the shrimp as they cook.
Using tongs or a slotted spoon, transfer the cooked shrimp immediately into the ice bath to stop the cooking process and set their texture. Let them sit for about 5 minutes until thoroughly chilled.
Drain the shrimp well and pat them dry with paper towels. Arrange the chilled shrimp on a serving platter, tails up or curled for an attractive presentation.
Meanwhile, prepare the cocktail sauce by combining lemon juice, ketchup, hot sauce, horseradish, Worcestershire, and a pinch of salt and pepper in a mixing bowl. Whisk gently until smooth and fragrant.
Taste the sauce and adjust the seasoning if needed—adding more lemon juice for brightness or hot sauce for extra heat. The sauce should be lively, spicy, and tangy.
Serve the shrimp chilled alongside the spicy citrus sauce in a small bowl. Garnish with lemon wedges or fresh herbs if desired for an extra touch of color and freshness.
Enjoy immediately to experience the full freshness, vibrant flavors, and appealing presentation of this spicy citrus shrimp cocktail.