In a frying pan, heat 2 inches of oil to 360 degrees F. Fry tortillas, 1 at a time, until crispy, about 2 minutes (do not fold tortilla). Drain on paper towels and set aside.
Brush tuna lightly with olive oil and season with salt and pepper. Grill until seared on the outside, rare in the center (2 to 4 minutes depending on thickness and how hot grill is). Remove and let cool slightly. Slice tuna on an angle.
Place a crisp tortilla on each plate. Top with a ladleful of black beans then with a layer of tuna. In a small bowl, combine watermelon, watercress, jalapeno, and radishes. Squeeze over juice of 1 lime and season with salt and pepper; toss. Divide equally among tostadas, sprinkle with crumbled feta and place a lime wedge alongside. Serve.
Vegetarian Black Beans:
In a large pot, bring black beans to boil in water to cover by 2 inches. Add half the onion, the celery and the bay leaf. Reduce heat and simmer until beans are tender, 1 1/2 to 2 hours. Strain and reserve liquid.
In same pot, heat olive oil and add bell pepper, remaining onion, garlic, green onions, basil, cilantro, soy sauce, lemon juice, cumin, cardamom, salt, and pepper. When vegetables are tender, add the beans and the reserved cooking liquid and simmer until reduced by half. Beans can be prepared up to 2 days ahead and refrigerated. To use, ladle out amount desired and heat until warmed through.