I'd recommend you use a product designed specifically to remove limescale like Hillmark Scalex. Whether you're using a specific product or hydrochloric acid you'll likely need to do a few applications to remove the bulk of the build-up. For the acid, you can apply it with a sponge and dab it over the area, it doesn't take much to start working. You can try a spray bottle too, but the acid will quickly ruin any seals in it.
Also, don't leave the acid on your bath for too long as it will start to etch into the coating.
Please use the utmost care and appropriate PPE with the hydrochloric acid and Scalex. Acid-resistant gloves, safety glasses, long sleeve shirt and pants and a well-ventilated area are all needed.