Prepare the Beer Batter: Mix all-purpose flour, rice flour, corn starch, salt, garlic powder, onion powder, paprika, and baking soda in a bowl. Place in the freezer for 10 minutes along with the beer.
Make the Tartare Sauce: Combine mayonnaise, chopped dill pickles, chives, tarragon, capers, Dijon mustard, Worcestershire sauce, pepper, diced shallot, and lemon juice. Mix well.
Prepare the Fish: Cut the white fish into chunks that fit your bun. Season well with salt.
Batter the Fish: Stream in the ice-cold beer into the flour mixture and whisk until smooth. Lightly flour the fish chunks before dipping in the batter.
Fry the Fish: Fry the battered fish at 375°F for about 4 minutes or until crispy. Immediately season with a little more salt after frying.
Assemble the Sandwich: Layer tartare sauce, butter lettuce, fried fish, and more tartare sauce on a bun. Top with the other half of the bun.