Preheat oven to 400 degrees F (200 degrees C). Spread potato nuggets out onto a baking sheet.
Bake in the preheated oven until nuggets are golden brown and crisp, 22 to 24 minutes.
Heat a large skillet over medium-high heat. Cook and stir beef in the hot skillet until browned and crumbly, 5 to 7 minutes. Add water and taco seasoning to beef; bring to a boil, reduce heat to low, and simmer until liquid reduces, about 5 minutes.
Set oven rack about 6 inches from the heat source and preheat the oven's broiler. Arrange potato nuggets on an oven-proof platter and cover evenly with ground beef; spread Mexican cheese and pepperjack cheese over the top.
Cook potato nuggets under the broiler until cheese melts, 1 to 3 minutes. Whisk sour cream and lime juice together in a bowl. Top potato nuggets with tomatoes, black olives, jalapenos, avocado, sour cream mixture, scallions, and cilantro, respectively.
