Halve the avocado, remove the pit, peel, and cut the flesh into small cubes. Place the avocado in a bowl and dress with the olive oil, lemon juice, a pinch of salt, and a generous sprinkling of black pepper.
Wash and trim the fennel bulb, then cut into small dice and add to the avocado. Add the well-drained, flaked tuna and mix gently to combine.
Arrange the tartare on four individual plates. Use a ring mold or small bowl to shape into neat rounds if desired, and garnish with mixed salad greens.