The biggest problem with desoldering things this big is the amount of heat needed to do the job. Make sure your iron is hot hot and that you focus on one connection at a time, get it really nice and hot to make sure that all the solder is melted and then a solder sucker will be able to clear the hole well enough.
Reducing the amount of metal that needs to be heated up always helps, so cut off the pins as low as possible from the solder side.
You will find the big lugs are the hardest to get clear as they are probably connected to the ground plane on the PCB and you will be heating up a lot of the board in doing the job. Maybe a combination of heat gun for the board and soldering iron to heat up the connection?
Another approach - you may want to sacrifice the pot (which actually looks like a rotary encoder) and get another. That give you the option to snip it off from the component side. 