Saute onion in 1 tablespoon hot olive oil in a large skillet over medium-high heat 5 minutes or until lightly browned. Add vinegar, 1/4 teaspoon salt, and 1/4 teaspoon pepper. Continue cooking until most of the liquid evaporates (about 2 minutes). Remove onion mixture from skillet; keep warm. Wipe skillet clean with a paper towel.
Sprinkle tuna with remaining 1/4 teaspoon salt and remaining 1/4 teaspoon pepper; dredge in flour. Heat half of remaining olive oil in skillet over medium-high heat. Add 4 tuna steaks to skillet; cook 2 minutes on each side or to desired degree of doneness. Repeat procedure with remaining olive oil and tuna steaks. Serve with warm onion mixture.