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 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.