Bring the water to a boil in a large saucepan. Add the barley; cover, reduce heat, and simmer for 15 minutes or until tender. Remove from heat; let stand for 5 minutes. Spoon barley into a bowl. Cool completely.
Sprinkle fish with 1/8 teaspoon salt. Place the fish in a small nonstick skillet coated with cooking spray over medium heat; cook 6 minutes on each side or until fish flakes easily when tested with a fork. Remove fish from pan; cool completely. Discard skin. Cut fish into 1-inch pieces; add to barley in bowl.
Place the remaining salt, arugula, and the next 4 ingredients (arugula through crushed garlic) in a blender, and process until smooth, scraping down the sides of blender. Pour arugula vinaigrette over barley and fish; add cheese. Toss gently to combine. Cover and chill.