Combine mayonnaise, minced chile, and lime juice in a small bowl; salt to taste. Refrigerate.
Cut tuna into 8 thin slices. Lay each slice between two pieces of plastic wrap and gently pound to 1/8 inch thick. Using a 2-inch round cookie cutter, cut out 12 circles of tuna, reserving scraps. Refrigerate.
Combine flour, cornstarch, and baking powder in a bowl. Pour in beer and stir gently with a fork until just combined. Let sit 15 minutes before using.
Mince tuna scraps and mix with shaved cabbage and enough lime-mayo mixture to moisten. Place most of crushed corn nuts on a plate. Place tuna circles on top of corn nuts to coat one side. Fill each tuna circle with a small scoop of tuna-cabbage mixture and carefully fold up into a taco shape.
Heat a saucepan with about 1/2 inch canola oil until very hot. Cut avocado into ¼ inch thick slices; place in beer batter, then transfer to hot oil and fry until golden. Remove with tongs to a paper-towel-lined plate and salt immediately.
To serve, sprinkle a bit of corn nuts down the center of each plate. Place a fried avocado on top, then place a “taco” against it. Garnish with dabs of mayo, minced lime segments, and cilantro. Serve with lime wedges.