No-win describes a situation where every choice looks bad. You can do this or that, and both will hurt. People almost always put it in the phrase “a no-win situation” (or “a no-win choice”). It is informal-to-neutral: fine in conversation and newspapers, a bit casual for a very formal essay. Though actually, speakers stretch it. They sometimes call a thing no-win when it is only hard, not truly impossible to come out well — a little drama in the word. The opposite picture in English is win-win, where both sides gain.