There are two different meanings for this sentence in English:
1. The dragon flies like a bird, and the dragon's tail is golden.
2. One of the dragons (the one with a golden tail) flies like a bird.
Using sentence C ("The dragon with a/the golden tail") creates meaning 2, whether "a" or "the" is used.
Using sentence B as written also creates meaning 2.
To create meaning 1, use sentence B and add commas or parentheses ("brackets" in BE):
B1: The dragon, whose tail is golden, flies like a bird.
B1: The dragon (whose tail is golden) flies like a bird.