Prep ingredients: Trim scallions, then finely chop. Finely chop 2 large garlic cloves. Reserve ¼ of the cilantro sprigs, then finely chop remaining cilantro leaves and stems. Zest and juice lime, keeping them separate.
Marinate shrimp: In a medium bowl, combine 2 teaspoons chipotle and half each of the lime juice and chopped garlic. Add shrimp, season with salt, and toss to coat.
Make beans & lime-yogurt: Rinse and drain black beans. In a medium bowl, combine beans, chopped scallions and cilantro, remaining chopped garlic, 1 teaspoon chipotle, 2 tablespoons vinegar, and 1 tablespoon oil; season to taste with salt. In a small bowl, stir together yogurt, lime zest, and remaining lime juice; season to taste with salt.
Make tostadas: Heat ¼-inch oil in a medium skillet over medium-high. Add tortillas to skillet, one at a time, and cook until brown and crisp, about 30 seconds per side (watch closely).
Cook shrimp: Carefully pour off all but 2 tablespoons oil from the skillet. Add shrimp and cook over medium-high, stirring, until just cooked through, about 2 minutes.
Assemble & serve: Spread lime yogurt on tostadas and top with black bean mixture, shrimp, and remaining cilantro whole sprigs.