Fill the tub 1/4 of the way full with hot water and add 1 cup of mild detergent. Mix the detergent into the water and let it sit for 20 minutes.
Clean the entire surface of the tub with a sponge to remove as much soap scum and dirt as possible. Drain the tub and thoroughly rinse it out with clean water. Dry the tub with clean towels.
Add white vinegar to a spray bottle. Spray it directly on the limescale in a mist. Get the limescale as wet as possible and let the vinegar sit on the affected areas for 30 minutes.
Scrub the limescale with a soft bristled scrub brush until it's completely removed. Rinse with clean water. This may take more than once to completely remove the limescale from the tub.