Heat frying oil in a 10-inch skillet to 350°F. Fry tortillas one at a time for 30 to 60 seconds per side until crisp and golden, holding them flat with tongs, then drain on a rack. Set the frying pan safely aside.
Brown beef, onion and jalapeno in a separate skillet over medium-high heat for 8 minutes until beef reaches 160°F, breaking it into small crumbles. Drain excess fat.
Stir in garlic, tomatoes, cumin, oregano, 1/2 teaspoon salt and water. Simmer for 6 to 8 minutes until tomatoes soften and the liquid becomes a moist coating around the beef.
Mash avocado with lime juice and remaining salt. Spread one-eighth of the avocado thinly over each crisp tortilla immediately before serving.
Divide warm beef among the 8 tostadas and add radish half-moons and queso fresco. Serve 2 per person while the shells remain crisp.