Heat olive oil in a heavy-bottomed skillet over medium heat. Stir in the onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Reduce heat to medium-low, and continue to cook and stir until the onion is very tender and dark brown, 15 to 20 minutes more. Remove the onion from the skillet.

Place the tuna steaks in the same skillet over medium-high heat and cook until golden brown, about 2 minutes per side. Remove the tuna steaks to a serving tray; keep warm.

Stir the vinegar and sugar together in the same skillet until sugar is dissolved. Return the onions to the pan, and simmer until the liquid reduces and is slightly thickened, about 5 minutes. Return the tuna to the pan and cook for 3 to 5 minutes. Place the tuna on the warm serving tray and top with the onion and sweet and sour mixture.