Boil the shrimp:
In a large pot, bring 2 quarts of water to a boil, salted with 1 tablespoon of salt. Add the shrimp and cook for 1 minute to 2 minutes max, depending on size of shrimp. (Over-cooking the shrimp will turn it rubbery.)
Remove shrimp with a slotted spoon and place into a bowl of ice water to stop the cooking.
Cut the shrimp, mix with lime and lemon juice:
Drain the shrimp. Cut each piece of shrimp in half, or into inch-long pieces.
Place the shrimp in a glass or ceramic bowl. Mix in the lime and lemon juice. Cover and refrigerate for a half hour.
Mix in the chopped red onion and serrano chile. Refrigerate an additional half hour. Right before serving, add the cilantro, cucumber, and avocado. Serve chilled with tortilla chips.