Prepare the Pico de Gallo:
In a large mixing bowl, combine the diced tomatoes, diced onion, chopped cilantro, and finely diced jalapeno.
Squeeze the juice of one lime over the top, season with a little salt, and toss it together with a spoon.
Add the cocktail sauce and stir until combined. Place the bowl in the refrigerator to chill while you prepare the shrimp.
Prepare the Shrimp:
If using cooked shrimp, skip to the next step. If using raw shrimp, place them in a colander, rinse with cold water, and drain well. Remove tails if necessary.
Bring a large pot of water to boil on the stove. Drop in about one tablespoon of salt. Add the shrimp and cook for about two minutes or until the shrimp is white with pops of pink.
Drain the hot water from the pot and cover the shrimp with cold water to cool them down and stop them from cooking further. Drain well and transfer the shrimp to a cutting board.
Cut each shrimp into two or three pieces. Reserve some of the shrimp for garnish and transfer the rest to the chilled cocktail sauce mixture. Stir well to combine.
Assemble and Serve:
When ready to serve, remove the pits and chop the avocados. Squeeze the juice from the remaining lime over the top of the chopped avocado.
To Serve in a Bowl: Garnish the top of the shrimp cocktail with the avocado, the reserved shrimp, and a little cilantro and allow people to serve themselves.
For Individual Servings: Layer a heaping spoonful of the shrimp cocktail mixture in the bottom of each glass. Add a generous layer of avocado. Fill the glasses to the top with more shrimp cocktail. Garnish each serving with a little avocado, cilantro, and a piece or two of shrimp.