Melt 1 tablespoon butter in a large skillet over medium-low heat. Drizzle in olive oil and add tilapia to the skillet. Cook until opaque throughout and then turn once, about 3-5 minutes. Cook for another few minutes and remove to a serving dish.
In the same skillet, add onions and garlic. Saute until the onions are translucent, about 5 minutes. Add in chopped olives and cook for another 2-3 minutes. Remove from the skillet and spoon on top of the tilapia or serve separately.