Combine cucumber, tomatoes, red onion, serrano peppers, and cilantro in a bowl. Add 1 teaspoon salt and squeeze 1 lime. Gently mix and set aside.

Squeeze the remaining limes into another bowl. Add remaining salt and pepper.

Bring a 1- to 2-quart pot of water to a boil. Place shrimp into the boiling water for 45 seconds. Quickly remove from the water using a strainer.

Chop the partially cooked shrimp into small pieces and add to the bowl with the seasoned lime mixture. Let sit for 20 minutes. Combine with the cucumber mixture and top with avocados.