I'm removing the Uber "tip" as it seems most people aren't having any luck with it. I did all of these on I Am Death Incarnate difficulty and you probably should too.
This is a video of the Caves Challenge Map in Wolfenstein: The Old Blood.
To obtain Gold, you must be playing on "I Am Death Incarnate" or "Uber" difficulty. The gold medal is rewarded at 26900. For higher scores go for headshots (600 points) and try to keep your combo active as you receive an extra 200 points for each kill in the combo.
After you kill all the enemies in the cave and head towards the elevator to exit the challenge, stop and wait as more enemies will spawn and run towards you. I was not able to get Gold without killing these enemies.