Most one-day Mumbai itineraries you will find online are written by people who have not tried to follow them. They ignore traffic, which in Mumbai is the single biggest constraint on your day.
The honest constraint: traffic
Crossing from South Mumbai to the northern suburbs can take ninety minutes in the wrong part of the day. Any itinerary that sends you back and forth across the city will spend more time in a car than out of it. The solution is to cluster your day geographically.
A realistic single day
Early morning: 6:00 to 8:00
Start before the city does. Sassoon Docks during the fish auction, or a flower market, gives you the best light and the fewest crowds of the entire day. This is the hour most visitors sleep through and later regret.
Mid-morning: 9:00 to 11:30
Dharavi. Two hours on foot is enough to understand the recycling, leather and pottery industries without exhausting yourself before lunch.
Midday: 12:00 to 14:00
Lunch and the South Mumbai heritage cluster. The Gateway of India, the Taj Mahal Palace, Chhatrapati Shivaji Maharaj Terminus and the Kala Ghoda district sit close together. You can walk between them.
Afternoon: 14:30 to 17:00
Dhobi Ghat, then Marine Drive. If you have any interest in architecture, the Art Deco buildings along the seafront are a UNESCO-recognised ensemble and most people walk past them without knowing.
Evening: 17:30 onwards
Chowpatty Beach at sunset, then a street food trail. Mumbai eats late and the food improves as the evening goes on.
What to skip if you only have one day
Elephanta Caves. It is a wonderful site but the return ferry alone eats four to five hours. Save it for a second day. The same applies to Film City and Sanjay Gandhi National Park, both of which are a long way north.
The realistic version
If you attempt all of the above you will be exhausted. Pick the morning cluster or the evening cluster and do it properly. Mumbai rewards depth more than coverage.