The meaning
> To slay means to kill violently
This man slayed several people when he tried to rob a bank
Or to impress strongly
Your jokes slay me
To overcome a seemingly insurmountable obstacle, to achieve something that seemed impossible.
To defend oneself in court
Etymology
> Slay the dragon comes from fairy tales, when a dragon either held a young beautiful princess as a hostage or threatened the castle of a King. There were usually one or two knights who would attempt to kill the dragon, but most failed. Finally here comes a Knight on to the scene, that would be successful in «slaying the dragon.»
Today, we figuratively use the expression, when we have some problem that we need to solve. Once we have finished working out the problem, or solving it, we have «slayed the dragon.»
Wrong translation
> Tuer ou faire rire le dragon… oui, les deux traductions littérales seraient correctes
Correct French idiom
> Il ne semble pas y avoir d’équivalent en français