Peel, devein, and wash the shrimp, then cut into bite-sized pieces (about ½-inch).
Place the bite-sized raw shrimp pieces in a non-reactive bowl (glass or ceramic).
Pour the lime juice over the shrimp, ensuring all pieces are covered. Toss gently to coat. Cover and refrigerate for 30 minutes, or until the shrimp turns opaque and pinkish.
While the shrimp is marinating, dice the mango, avocado, cucumber, and jalapeño. Chop the cilantro.
After the shrimp has marinated for 30 minutes, drain about half of the lime juice and lemon juice (keeping some for flavor). Add the diced mango, cucumber, pickled red onion, and jalapeño to the bowl with the shrimp.
Add salt and black pepper. Gently toss to combine all ingredients.
Gently fold in the diced avocado and chopped cilantro. The avocado is added now to prevent it from breaking down too much.
Cover and refrigerate for an additional 10-15 minutes to allow flavors to meld.
Taste and adjust seasoning if necessary before serving.