vedikaseth Bombay rains are harsh! The one thing you can do is use flexible covers that work similar to roller blinds, and are transparent which allows the light to enter. There are many companies that offer such a product. Just choose one where the installation is easy and taking down the sheets is not an issue once the rains are over. Do keep in mind however that the water will still enter the balcony, you will simply be reducing the force of rains, and will require a water outlet.

This is shingle roof, its actual pic from my Resort project in Goa

Although it does not attract much attention, so can be left as it is. But if client wants to get it done...Have you consider vines instead like English ivy kind of plants? Although it might be difficult to find any long enough to cover the area. You could drip irrigation for them. Another option is to get a wall build according to the curves but again that would mean changing the exterior. I would not recommend fiber options. They don't look good. You can work around with metal pipes to create a new look too

Looking for polycarbonate or PUF sandwitch roofing experts and vendors in Kolkata. Can you pls help with contact details.