What does it mean to be someone's bulldog?
I was going to point you at a dictionary, but I haven't found one that has this meaning (even the OED).
It is an extension of the meaning "[a person] that possesses the obstinate courage of the bulldog."
Here it means that he is obstinate and probably aggressive in defending Darwin: acting as a sort of guard dog.
Edit: as pointed out by Michael Harvey in a comment, it is more than this. Huxley was known for actively attacking opponents of Darwin, and described himself as "Darwin's bulldog".