You have to enter "The Enigma" than do as follows:

1. Shoot the switch to enter the second room.
2. Use Fireball to open the second room and head into the next one.
3. In the room with the Silver Key, notice the colored platforms (red, blue, yellow).
4. Step on the platforms in this order (yellow, blue, yellow, red, blue, red, blue, red).
5. Go through the door directly in front of you to get the Gold Key (it will be down a long walkway).