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