No Vinegar Allowed challenge requires you to promote out of the ladder when your vinegar_count would reach 0.
This challenge is another ultimate walling challenge and it is quite a hard one.
Vinegar starts decaying when the ranker reaches top-1 position and holds it.
Vinegar decays at a 0.25% of current vinegar_count per second which makes it independent of grape_count and vinegar_count sizes. Therefore, in order to drain your vinegar_count to 0 you would need to hold the top for more than 30 (!) minutes.
But there is a second, easier and faster way: you can perform a so-called 'leapfrog' move.
Basically, what that means is whenever the other ranker holds the top position and you are right behind them, you can try to throw vinegar at them and, if that was a successful attempt, instantly promote.
Winning might be troublesome depending on how often you would be able to use a leapfrog move to get rid of your vinegar.