Here are some ideas ~ you didn't say if it was fiberglass or porcelain so I found what I thought might work
what is it made of Porcelain,Marble, Fiberglass,Acrylic,Copper,Galvanized metal ??
Need more info please.
There are paint kits for bathtubs. Read all directions and gather all other needed supplies. Head the dry times
The best thing I found for tub scratches is plain old ajax scouring powder.