Combine 1/2 cup vinegar with 1/2 tsp. liquid dish soap in a small bowl. Swish the mixture thoroughly to make sure it's well mixed.
Dip a cleaning cloth into the mixture, and then wipe down the vinyl tub enclosure with the cleanser. Allow the solution to work on the grime for several minutes before proceeding.
Rub the vinyl tub enclosure with the cleanser-covered cloth, and then wipe the mixture away with a clean, wet cloth.
Sprinkle baking soda on any areas that are still grimy. Scrub gently with a nylon scrubber, and then rinse away that residue as well.