Place eggs in a large saucepan. Cover with water to 1 inch above eggs. Bring just to a boil. Remove from heat; cover and let stand 15 minutes. Drain; cool in ice water 5 minutes. Peel eggs; cut each egg into 4 slices.
Place potatoes in pan; cover with water. Bring to a boil. Reduce heat; simmer 12 minutes. Add beans, and cook 3 minutes. Drain; plunge beans into ice water for 1 minute. Drain well.
Heat a large cast-iron skillet over medium-high heat. Coat pan with cooking spray. Sprinkle tuna with 1/4 teaspoon salt and pepper. Add tuna to pan; cook 2 minutes on each side or until desired degree of doneness. Cut thinly across the grain.