For the pico de gallo: Mix together the tomatoes, capers, olive oil, lemon juice, cilantro and onions in a large bowl. Season with salt and pepper.
For the radishes: Slice the radishes in half lengthwise, then into thin half-moons (and a few into quarter moons, if you want, for varied texture). Toss the radishes together with the anchovies, parsley and olive oil in a large bowl. Season with salt and pepper.
For the fish tacos: Preheat the oven to 350 degrees F. Whisk together the flour, semolina flour, baking powder, sea salt and some pepper in a large bowl. Slowly whisk in the beer and set aside.
Add enough canola oil to a large cast-iron or other low-sided skillet to come halfway up the sides. Heat the oil to 350 degrees F. (Use a deep fry thermometer to be sure - or do it the grandma way and add a piece of bread to see if it fries and browns - if it does, it's ready).
Slice the tilapia into 1/2-inch strips or "finger"-size pieces.
When the oil is hot, dip each piece of tilapia into the batter using tongs, allowing excess to drip off. Carefully add to the hot oil one piece at a time. Fry in batches until golden brown and the fish is cooked through, 3 to 5 minutes. Remove from the oil with a slotted spider or skimmer and drain on a paper-towel-lined baking sheet.
Meanwhile, warm the tortillas by wrapping them in foil and placing them in the oven for 10 minutes. To serve, place one piece of fish on a warmed tortilla. Top with shredded lettuce and an avocado slice. Serve with a lemon wedge, pico de gallo and radishes with anchovies.