Bring 1 quart of heavily salted water to a boil. Scoop in the shrimp, cover, and let the water return to the boil. Immediately remove from the heat, set the lid askew and pour off all the liquid. Replace the cover and let the shrimp steam off the heat for a few minutes if they are not cooked as much as you would like. Spread them out to cool completely or, for the crispest texture, immediately dunk the shrimp into an ice bath.
Into a medium bowl measure in all the ingredients. Mix in the cooled shrimp. Taste and season with salt if it needs it. Cover and refrigerate if not serving immediately.
Spoon the shrimp cocktail into sundae glasses, martini glasses or small bowls; garnish with a little chopped onion and cilantro. Serve with tostadas, tortilla chips or saltines to enjoy alongside.