What is the shell material? What brand? What color?
For acrylic, a 50/50 mix of muriatic acid added to water. And, of course, time and elbow grease. The more time the less elbow grease.
DO NOT USE A SQUIRT BOTTLE. Acid mist is BAD. You can soak a WHITE rag and let it sit for little while on the tough spots.
On a plastic shell I would make it a 25% acid mix and use more elbow grease than time.
I have no personal experience with it but I have heard that acid can discolor plastic shells. So a weaker mix and less exposure time (so more scrubbing) is the way to go. Use a plastic bristle brush not a kitchen scrubbie.