Place the first 3 ingredients in a 6-qt. electric pressure cooker. Lock lid; close pressure-release valve. Adjust to pressure-cook on high for 8 minutes. Quick-release pressure. A thermometer inserted in chicken should read at least 165°.
Remove chicken; shred with 2 forks. Return to pressure cooker. Stir in cream cheese, salad dressing, sour cream and 1 cup cheddar cheese. Sprinkle top with remaining cheddar cheese, blue cheese and green onions. Serve with tortilla chips.