Did any Boeing 787 operator achieve the 20% fuel efficiency improvement over the 767?
You have not defined your benchmark/reference value, but a three-year-old article suggests this was possible depending on definition even at a very early stage for some airlines:


  ANA earlier this month was the first to reveal that its aircraft were producing around 21% lower fuel burn on international flights compared to the 767-300ER that the 787 is designed to replace.


They also say however: 


  After its first six months of service, ANA says the 787 efficiency levels are slightly up on the 20% savings originally expected at the beginning of the program. On domestic routes, the saving is 15-20%, which meets expectations, say ANA officials.