Bring about 6 cups of salted water to a boil.
Fill a separate mixing bowl with ice water and set aside.
Add the shrimp to the boiling water and cook for 1 to 2 minutes, or until shrimp are pink and opaque.
Using a slotted spoon, remove shrimp from the water and transfer to the ice water to stop the cooking.
Drain and chop the shrimp into about ½-inch pieces, then transfer them to a ceramic bowl or glass bowl.
To the shrimp, add in the lime juice and lemon juice; cover and refrigerate for 30 minutes.
Remove from the fridge and stir in the tomatoes, jalapeno pepper, red onions, cilantro, salt, and pepper.
Cover and refrigerate for 20 to 30 minutes.
Add in the cucumber and avocado; toss to combine.
Taste for salt and pepper, and adjust accordingly.
Serve with tortilla chips.