Pat the 4 tilapia filets dry with paper towels. Set aside 1 tablespoon of the butter for later use.
In a large skillet over medium-low heat, melt 1 tablespoon butter and add 1 tablespoon olive oil, swirling to coat the pan.
Add the tilapia filets in a single layer (do not overcrowd). Cook until the bottom is set and the edges look opaque, about 3–5 minutes.
Carefully flip each filet and cook the second side until the fish is opaque throughout and flakes easily with a fork, about 3–5 more minutes. Transfer the cooked filets to a serving dish and keep warm.
Return the skillet to medium heat and add the reserved 1 tablespoon butter. When melted, add the 1/2 diced onion and the 2 chopped garlic cloves.
Sauté the onion and garlic until the onion is translucent, about 5 minutes.
Add the 1 cup chopped olives to the skillet and cook, stirring, until heated through, about 2–3 minutes.
Spoon the olive-onion mixture over the tilapia filets (or serve it alongside).