A no-win scenario or no-win situation was a situation in which every possible outcome was undesirable.
In the 2250s, acting captain Saru of the USS Discovery gave a speech to his crew, after discovering the betrayal of Captain Gabriel Lorca, in which he told them that they would not accept a no-win scenario. Sylvia Tilly and Paul Stamets later repeated Saru's words. (DIS: "What's Past Is Prologue")
The Kobayashi Maru scenario was one example of such a quandary, though James T. Kirk, as well as his alternate reality counterpart, said he didn't believe there was such a thing. (Star Trek II: The Wrath of Khan; Star Trek)
While taking the bridge officer's test in 2370, Deanna Troi was initially frustrated by the engineering qualification, which involved ordering a crew member to their certain death. Before ultimately passing the test, she asked William T. Riker if there was a solution to the problem, or if it was testing her ability to handle a no-win situation. (TNG: "Thine Own Self")
In 2371, after their "starship" was shot down, Kenneth Dalby described the circumstances in a simulation he and several other former Maquis were undertaking as a no-win situation, feeling there was nothing else they could have done rather than go out in a blaze of glory. Tuvok, their instructor, disagreed, suggesting retreating was a viable option. (VOY: "Learning Curve")