Cebu Pacific Airlines
Domestic air travel is cheap in the Philippines. Getting to Palawan from Cebu is only going to cost around 1400 to 1500 peso.
The departure tax at the Cebu airport on Mactan Island is 200 peso.
Keep in mind that the airport is a fair distance from town so allow enough time to get there. There is a 45 minute cut off time for checking in before the airline will let your seat go to those on standby.

Cebu Pacific leaves for Puerto Princesa 3 times a week from Cebu.
Domestic flights are a good value in the Philippines and so much easier than taking the boat or bus!
There is a major expansion at the airport in Puerto Princesa because tourism is expected to boom in the coming years. Domestic and international flights to Palawan are expected to to increase dramatically.
I have traveled to Palawan by ship from Iloilo and Manila several times, but getting there that way is only for those with a lot of time on their hands and a lot of patience.

The only complaint I have with Cebu Pacific, is that booking online can be troublesome.
In Cebu there is a Cebu Pacific ticket office in the Robinson Mall that I have used several times.
The line is long but you can take a number and go get something to eat and then come back – just be back before your number is called.
Cebu Pacific Airlines
Climbing Mount Apo
General Santos
Judy's Resto Bar
Logging with Motorcycles
Mount Mayon
Biri Island
Calbiga Cave
Mangrove Swamp Palawan
Mikes's Resort