Preheat the oven to 450 degrees F (230 degrees C). Place catfish on a baking sheet.
Roast in the preheated oven until flesh is opaque, 10 to 15 minutes. Flake into large pieces with a fork. Lay the flaked fish out on a plate to dry.
Heat oil in a large pan over medium-high heat. Fry fish in batches until golden brown, about 5 minutes. Try not to break up the fish too much in the pan.
Toss mango, shallots, cilantro, green onions, peanuts, fish sauce, lime juice, Thai chiles, and sugar together in a large bowl. Toss in crispy catfish at the very last minute. Check the seasoning; the salad should taste sour, hot, and salty, with a slight sweetness at the end.