Place the shrimp in a bowl and decide whether to leave them whole or chop them into smaller pieces depending on your preference. Pour the lemon juice over the shrimp, ensuring they are fully covered.
Cover the bowl and refrigerate until the shrimp turns opaque and slightly firm, indicating it has cured in the citrus.
Add the chopped onions, tomato, cucumber, radishes, and minced garlic to the shrimp. Toss everything gently so the ingredients are evenly distributed.
Gradually mix in the jalapeños and cilantro, tasting as you go to control the level of heat and freshness.
Pour in the tomato and clam juice cocktail until you reach your preferred consistency, whether slightly saucy or more brothy.
Cover the mixture again and refrigerate until well chilled and the flavors have blended together.
Serve cold with tortilla chips on the side for scooping.