Learjet 35 First Officer reported loss of hydraulic pressure and return to departure airport.

Narrative

Aircraft X was conducting a ferry flight from ZZZ to ZZZ1; and had been level at FL260 for roughly nine minutes. During the climb and since reaching altitude a continuous whistle was heard from the main cabin door seal. I had also previously set the cabin altitude selector to the position corresponding to FL280; and reset the selector to FL260. The whistle continued; and I rotated the selector above the FL260 position; then below the FL260 position; then back to FL260 to make sure the setting was actually selected.About a minute later I realized that the cabin felt significantly cooler; and I looked down at the environmental panel to see where the temp needle was set; and noticed the cabin altitude increasing past 3;000 feet. I pointed it out to the PIC (Pilot in Command); and watched as the needle continued climbing at a steady rate; reaching 9;000 feet cabin altitude in about twenty seconds. The PIC called for oxygen masks and began to don his mask; and I did the same a moment later. At this time the cabin masks also deployed and the cabin altitude reached 15;000 feet.Pilot monitoring advised ATC for loss of cabin pressure and let ATC know that we needed to descend; while I disconnected the autopilot and initiated a descent at about 3;000 FPM. We continued the descent along our previous course; but decided that we would return to ZZZ once we reached a lower altitude. Once below 12;000 feet we both removed our masks; and continued to ZZZ at 11;000 feet for an uneventful landing. During the transit back it was noted that we maintained about a 9;000 foot cabin altitude.