I've read all about how invincible the Mongol push was into a vast area of central Asia, Eastern Europe, Far and Middle East.
Are there any examples where they met an adversary and were beaten badly?
The Battle of Ain Jalut (1260), against Mamluks in modern-day Israel, resulted in the Mongol forces sent to that battle being completely destroyed. I don't know much else about it, but that's one example of a decisive victory against the Mongols.