Bring a large pot of water to a boil. Pour in the beer and Old Bay and stir. (The beer will cause the pot to fizz up a bit, don't worry.)
Add the shrimp and cook for 3-4 minutes until pink and tender. Remove the shrimp from the water with a spider strainer or pour the pot out into a colander.
Transfer the shrimp to a bowl and cover with plastic wrap or foil. Place in the fridge until chilled, about 4 hours to overnight.
Cocktail Sauce
Stir all the sauce ingredients together in a medium bowl until evenly combined. Adjust to taste with more horseradish, lemon juice, or hot sauce as desired. Cover and chill until ready to serve.
Notes
Nutritional information is for 0.25 pounds of shrimp and 2 tablespoons of cocktail sauce.
The shrimp can be made up to 24 hours ahead of time and kept covered in the fridge until you're ready to serve.
Don't place the shrimp in a water bath. This will remove some of the seasoning/flavor. If you need a quick cooling option, place a glass or metal bowl in a water bath and put the cooked shrimp in the bowl.
You can use tail-off or tail-on shrimp. Jumbo shrimp (21/25) or extra large shrimp (25/30) are recommended but you can use large shrimp if they're on sale.