tilt at windmills

From a passage in the novel Don Quixote where the eponymous character tilts (i.e. jousts) at windmills that he has mistaken for giants.

tilt at windmills (third-person singular simple present tilts at windmills, present participle tilting at windmills, simple past and past participle tilted at windmills)

1. (idiomatic, intransitive) To attack imaginary enemies.

   Synonym: fight windmills

2. (idiomatic, intransitive, by extension) To go on a wild-goose chase; to persistently engage in a futile activity.

   Synonym: chase a rainbow