Bring a medium saucepan filled with water to a boil. Carefully add eggs to pan; cook 6 minutes. Add green beans; cook 2 minutes. Drain; plunge bean mixture into a bowl of ice water. Let stand 3 minutes; drain. Peel eggs, and cut into quarters.
Heat 1 1/2 teaspoons oil in a large nonstick skillet over medium-high. Sprinkle fish with 1/4 teaspoon salt and 1/8 teaspoon pepper. Add fish, skin side down, to pan; cook 7 minutes. Turn, and cook 3 minutes. Remove fish from pan; break into large flakes with a fork.
Combine remaining 2 1/2 tablespoons oil, remaining 1/4 teaspoon salt, remaining 1/8 teaspoon pepper, vinegar, parsley, and mustard in a bowl. Divide lettuce among 4 plates; top evenly with eggs, beans, cucumber, corn, olives, radishes, and fish. Drizzle with vinaigrette.