Something like this image for example. Is this possible without any sort of editing? https://www.instagram.com/p/BcWg4HYgRn8/?taken-by=jadgghorayeb
Yes, it is possible.
The key to getting the reflection to mirror all of the subject at the same size is to shoot at as low an angle to the surface of the water or other flat, reflective surface, as possible.
The higher the camera is above the reflective surface and the larger the angle between the lens' optical axis and the reflective surface, the greater the difference will be between the size of the subject and the size of the subject's reflection, due to the different optical distance from the subject to the camera when compared to the optical distance from the subject to the reflective surface to the camera.
I'd guess that the example image to which you linked was taken with the lens just a few centimeters above the surface of the water. Even so, the reflection of the leg perpendicular to the water is about 3% shorter than the leg itself is above the water.
Absolutely it is possible. Do an image search for "mountain reflection water", to see countless examples. Here's one of Mount Hood reflected in Mirror Lake, Oregon, U.S.A, from Wikipedia:
From Wikimedia Commons, Public Domain from US Federal Highway Administration
Not not convinced they weren't edited to get the effect? Add "Ansel Adams" to the search, to get examples that were done on film about 80 years ago. Adams's Mirror Lake, Mount Watkins, Yosemite National Park is a particularly good example.