Heat a large skillet over medium-low heat and melt 1 tablespoon of the butter.
Add the olive oil to the skillet, then place the tilapia filets in a single layer.
Cook the tilapia until opaque on the bottom, about 3–5 minutes, then flip and cook until cooked through, another 3–5 minutes; transfer to a serving dish.
In the same skillet, add the remaining 1 tablespoon butter if needed, then add the diced onion and sauté over medium heat until translucent, about 5 minutes.
Add the chopped garlic to the onions and cook until fragrant, about 30 seconds to 1 minute.
Stir in the chopped olives and cook for 2–3 minutes to heat through and blend flavors.
Remove the topping from the skillet and spoon it over the cooked tilapia, or serve it alongside.