Heat vinegar, sugar, salt, and seasonings in a saucepan to boiling, stirring occasionally. Remove from heat; pour into an 8-in. square glass or ceramic baking dish. Let cool.
Sprinkle fish with pepper. Heat a large nonstick frying pan over medium heat. Add 1 tbsp. oil, then add fish and cook, turning once, until barely cooked through, 3 to 6 minutes. Pull off skin and discard.
Transfer fish to pickling mixture, cover, and chill 2 hours; turn fish after 1 hour.
Toss arugula with remaining 1 tbsp. oil and 2 tsp. pickling mixture in a large bowl. Arrange on plates. Using a slotted spoon, arrange fish next to salad. Serve with radishes, butter, and bread.
Note: Nutritional analysis is per serving.