Preheat a grill to medium. Brush the tilapia and onion with 1 tablespoon oil. Add the onion to the grill and cook, covered, until tender and grill marks appear, about 5 minutes. Coarsely chop the onion and transfer to a medium bowl. Add the shredded cabbage, carrot, lime juice, sugar and remaining 1 tablespoon oil; season with salt and toss well.
Season the tilapia with salt, arrange on the grill, cover and cook until opaque, about 5 minutes. Flake the fish and toss with the cabbage mixture. Divide the slaw among the 4 whole cabbage leaves; top with the salsa verde.