I think the fastest, cheapest and easiest fix would be to:
1. Kill the mold and mildew on the drywall with bleach, straight out of a jug, and allow to dry overnight or longer.
2. Install an inexpensive tub surround, which you can buy for about $100 from any place that sells bathroom fixtures.
Plastic tub surrounds come in either 3 piece kits of 5 piece kits. A 3 piece kit will have a plastic panel for the front, side and back walls of the shower. A 5 piece kit will also have front and back corners that will have shelves on them for shampoo, creme rinse, soap, etc.