If you are not starting with pre-cooked shrimp, then start with peeled, deveined raw shrimp and boil in clam juice (1 to 2 bottles) on the stove for about 2 to 3 minutes until it turns a light pink, and then drain, and let cool before adding with the rest of the ingredients.
In a large bowl, combine everything but the avocado. Stir well to combine.
Cover and refrigerate for 2 to 3 hours before continuing and before adding avocadoes.
Add the avocados and gently stir.
Garnish with cilantro, lime wedges, and a few pies of shrimp. Serve cold with crackers, tortilla chips, and lime wedges.
Boil Shrimp. While you can boil the shrimp in the water, to add extra flavor boil the shrimp in clam juice, and save some of that clam juice to add into the shrimp cocktail.
Don't Overcook Shrimp. Shrimp cooks very quickly. When you add the shrimp to the boiling claim juice, watch it the whole 2 to 3 minutes, stirring every so often. It is ok if the shrimp is a little undercooked because it will finish cooking while mixed into the shrimp cocktail because of the acidity of the lime and tomato juice.
Shrimp Tails. It is your choice to leave the shrimp tails on or to remove them. I usually remove the tails on most of them, but leave a few shrimp with tails on and place them on top of each Mexican Shrimp Cocktail.
English Cucumbers. If you are using English cucumbers, the skin is mild and tender, so you can leave the skin on. However, if you are using regular cucumbers, then you would want to peel the cucumbers before adding them to the shrimp cocktail.
Refrigerate. For even more flavor, once you have all the ingredients mixed together, except the avocado, refrigerate for 2 to 3 hours to let the flavor more fully develop.