Ok so it does in fact seem you are using ataraxia to describe a specific type of being untroubled (about gods and death primarily, but maybe including a few other things), and that you don't include the trouble of the sharp pain of advanced kidney disease to be within the scope of the word.
Correct. Ataraxia appears to be achieved by rooting out fears and anxiety, leaving the mind to be free of those disturbances.
PS. I would also include that it is achieved as well through an understanding of natural science and how the world works, including celestial and meteorological phenomena, and also living virtuously. It is having the mind in a secure harbor, undisturbed by fears and anxieties.