I'm writing a short hard-science story about an organism that loses most of its water much like tardigrades before entering dormancy but this organism is the size of a cat, how could I explain this using hard-science?
Your organism can simply stop assuming water and let perspiration and excretion remove water from its body, aiding the process with something that goes against the osmotic gradient.
The first part is similar to what Anastatica does, while the second is similar to what some desert animal does to concentrate its urine, the only difference is that instead of concentrating the waste it should concentrate the body.
1.Sweat it out: Your animal would need to have the ability to sweat. It could have additional dormant sweat glands that only activate when the creature is preparing for dormancy. It would then seek out hot places, start moving frantically, and/or experience muscle spasms in order to raise its internal temperature.
2.Evaporate it: The creature may have semipermeable skin akin to a frog's. Before it enters the dormant state, it simply crawls out of its humid environment and waits for the sun to do the work.
If you don't want your animal to rely on humid environments, it may have a way to expose a large amount of its mucous membrane, similar to opening its mouth wide.
3.Expel it: The animal may have control over its potassium-sodium-magnesium levels. The balance of these minerals plays a role in water retention. You can look into what some sports professionals eat to get rid of "water weight". Apparently, dandelion supplements, as well as foods like celery, coffee, tea, and many others, will increase the amount of urine produced.
Now, we have successfully rid the animal of moisture.
Unfortunately, it died.
The miraculous hardiness of tardigrades and other extremophiles is mostly due to their simple internal makeup. Anything as large as a cat would need much more complex physiology to sustain its body. However, more complexity also means more vulnerability.
Another secret to extreme hardiness seems to be trehalose, an energy-dense type of sugar. How exactly trehalose works in an organism entering anabiosis is unknown, but it is theorized that dehydrating organisms gradually replace their body water with trehalose. In order to do this, an organism needs the ability to synthesize it internally.
What are the largest and most complex organisms that can produce trehalose? Flying insects. They use trehalose as a blood sugar, as it is very energy-dense and serves as an energy source for flying.
In order to have a cat-sized animal capable of anabiosis (or at least have all the puzzle pieces we know of), you would need an environment that allows for giant-sized insects.
I imagine your animal as a type of terrestrial (so it does not use up it trehalose for flying) bug. It would obviously have to go with option 2. It could have soft permeable body hidden under hardened elytron and when it needs to get rid of the moisture it would expose the body to sun, gradually geting sundried.