Step 1Combine the fish bones, onion, celery, garlic, bay leaf and peppercorns in a large stockpot. Add enough cold water to cover. Bring to a boil. Skim off the foam. Reduce the heat and just barely simmer for 45 minutes. Strain and discard the solids. The stock should measure about 2 quarts.
Step 2Combine the stock, chicken broth, tomatoes, mushrooms and paprika in a saucepot. Bring to a simmer. Cook 10 minutes.
Step 3Remove the tough ribs from the chard. Cut each chard leaf into large dice. Add the chard to the soup and simmer 10 minutes. Add the swordfish and halibut and gently simmer about 5 minutes. Add salt to taste and garnish with the basil.