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As stated below you do not need a visa for Hong Kong. Get a double entry visa for Shanghai and Beijing, apply to the agents in London, cost this year is £75 each and the service is very quick. I would imagine applying through Princess would add an extra charge. You will not be allowed to board the ship without the visa. Vietnam also needs a visa but this done automatically on ship and costs $11 each. Enjoy the trip, it is something different!
We did this cruise last year and we had to get a double entry visa for China you do not need a visa for Hong Kong. The cruise company we book with sent us all the relevant paper work and where to send it we also received it from Princess. We had a great time fabulous cruise. Enjoy.