In a large bowl, combine the drained tuna, soy sauce, cilantro, pepper, garlic, breadcrumbs, and eggs. Mix, using your hands, until fully combined. Mixture should form patties easily and without breaking.
Form the patties by dividing the mixture into four sections. Roll each section into a ball, then press into a 1-inch patty. Set aside.
To make the cucumber sauce, drain the cucumber by squeezing between paper towels. Discard excess water and add cucumber to a bowl with the yogurt, dill, oil, and lemon. Mix well to combine, then season to taste with salt and pepper.
To cook the patties, heat thin layer of oil in a skillet over medium heat. Add the patties and cook until browned, about 5 minutes per side.
Place patties on bottom bun. Cover with cucumber sauce, then top with red onion and sprouts. Complete with the top bun to serve.