Rinse the sushi rice under cold water until the water runs clear. Combine the rice and water in a rice cooker or saucepan and cook according to package instructions. Once cooked, let it cool slightly.

In a small bowl, mix rice vinegar, sugar, and salt until dissolved. Gently fold this mixture into the warm rice and set aside to cool completely.

In a mixing bowl, prepare the tempura batter by combining the tempura batter mix with cold water until smooth.

Heat about 2 inches of vegetable oil in a deep pan over medium-high heat. Dip each shrimp into the tempura batter and carefully place them in the hot oil. Fry until golden brown and crispy, about 2-3 minutes. Remove and drain on paper towels.

To assemble the rolls, place a bamboo sushi mat on a flat surface. Lay a sheet of nori on the mat, shiny side down. Wet your hands and spread a thin layer of sushi rice over the nori, leaving about 1 inch at the top edge.

Arrange a few slices of avocado, cucumber, and 2-3 pieces of fried shrimp in a line across the rice. Using the mat, carefully roll the sushi away from you, applying gentle pressure to keep it tight. Seal the edge of the nori with a little water.

Repeat with the remaining ingredients. Slice each roll into 6-8 pieces with a sharp knife. Serve with soy sauce, wasabi, and pickled ginger.