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 an 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")