Mate, the drive up to those alpine lakes is no joke, the roads turn into gravel and mud pretty fast once you leave the main highway, so a city hatchback is a terrible call. Sorting the paperwork for renting a car in Kyrgyzstan before you even pack your boots is the smartest play. You just land at Manas airport, grab the keys to a proper diesel 4x4, and head straight for the mountains without losing a day. Have a look at the SUVs up for grabs right here
https://getrentacar.com/en-US/kyrgyzstan .