I want to visit shenzen, shanghai and Hong Kong starting from Singapore.

Grant, you can make the visits to all the mentioned cities, but you will have to change the order of visits of some of them.

For example, you cannot use visa free transit by taking an overland transport from Hong Kong to Guangdong province. I other words, you will do much better by flying first to Shenzhen and then to take a ferry to Hong Kong. Like this, you will be eligible for 144 hour visa free transit. Of course, you will need to book a ferry ticket online in advance and use exactly that ferry you have bought your tickets for. To conclude, your first 144 hour visa free transit itinerary will be:

Singapore - Shenzhen - Hong Kong

Also, this order will allow you to be eligible for your second part of journey and that is a visit to Shanghai. So, your second segment will be:

Hong Kong - Shanghai - X country

This option is also eligible for Shanghai area, but you will have to decide where you will fly after Shanghai. In other words, your next destination after Shanghai has to be a city in a country or eligible territory outside both mainland China and Hong Kong. Of course, you can take a direct, nonstop flight from Shanghai to Singapore.

Also, you will need all those tickets in your hand before your departure from Hong Kong.

As you can see, this is doable, but with necessary corrections to be eligible for 144 hour visa free transit in both Shenzhen (Guangdong province) and in Shanghai area.

You will need to apply for a visa since you are not in transit to third country.