Possible lift mechanisms for pop up tops. I'll ignore the types that won't work for a hard sided pop up. That is any one that doesn't raise and lower the top uniformly.
Cable lift: Uses uses cables and sliding telescoping bars with pulleys at their ends. Works well, and is cheap to make in volume, but difficult for small runs. Lifted height can easily be taller than twice unlifted height. Weight limited by the strength of the components. You could scavenge the mechanism from an existing pop-up camper. The cables for each corner would be clamped together with one proceeding on to a winch which is used to raise and lower the top. Conceptually the simplest, and if you scavenge the lift columns from a old pop up camper likely the easiest to make, and repair with parts available world wide.
Hydraulic cylinders at each corner: Easy to install, height usually limited to a few inches shorter than unextended cylinder length unless dual stage cylinders are used. They increase cost allot. Balancing the hydraulic fluid flow to each cylinder requires a special splitter. While raised you should support the top by other means as fluid will flow though the splitter from cylinder to cylinder and the top may jam or get out of alignment. A hydraulic pump and reservoir are needed. An advantage of using this system is the hydraulic pump can be mounted high and out of the way of water, and all mechanisms below could be waterproofed.
Coil spring in tubes: Harder to install, as conduit tubes need to be bent and installed for each corner. Could still be home built, but savaging the mechanism from a pop up camper is possible. Lift height is limited to the length of the machine screw used to push on the springs. Principal is you have a coil of spring which is pushed through a tube. When you push on one end, the other end moves because each wrap of the spring rests against the neighboring ones. The hard part is the mechanism to push on the springs. It could use a machine screw and crank, or a cable and crank. The machine screw needs to handle the full load of the top in compression so a cheap bolt style threaded rod won't do. Look for "machine screws" or "lead screws".
Machine screws are available from many sources and near the cheapest can be used as no precision is needed, just reasonably smooth operation. At one end of the rod is the crank handle and a thrust bearing. The thrust bearing is firmly mounted to the camper. On the machine screw is a traveling bearing. It moves in a rectangular tube. Attached to that traveling bearing is a plate that just fills the inside of the rectangular tube. The plate is attached to one end of each of the 4 springs used to push the top up. At the far end of the rectangular tube each of the coil springs goes into it's own conduit. That conduit is routed to it's own lift point. The spring exits the conduit going straight up. Usually a set of telescoping tubes is used to contain it as it is pushed out the end of the conduit so it doesn't bend.
This patent shows a similar system, but it uses a cable to pull on the spring ends for moving them to raise the top.
US Patent 5769485 - Page 1 Image - Top lift system for pop-up campers Nice picture diagrams. You can see the telescoping tubes in figure 3 on page 4. The method of actuation I described with the machine screw is no longer patented. There is also a cable drawn version with the springs all brought together like the machine screw one uses. It too should be no longer patented. I do like this design as it reduces the mechanism to two identical units.