Answers B and C can be eliminated because of their awkward structure and the unnecessary use of "-ing" forms.
Answer D wrongly uses "that" to refer to "Jerusalem to be destroyed."
Answer A is the most concise. Moreover, it is grammatically and stylistically correct.

sana.noor wrote:On seeing Halley's comet in A.D.66, the Jewish historian Josephus was persuaded that the apparition was a portent of the destruction of Jerusalem, which in fact took place four years later.

(A) of the destruction of Jerusalem, which
(B) of Jerusalem being destroyed, which
(C) for Jerusalem being destroyed, and that
(D) for Jerusalem to be destroyed, and that
(E) for the destruction of Jesuralem, and it

WHICH vs THAT split here. If we use THAT then the constrction will become "Josephus was persuaded THAT XX (the apparition was...Jerusalem) and THAT YY". This means Josephus was persuaded for both XX and YY. But the intent is not to say that Josephus was persuaded for YY as well. Intent is only to say tht Josephus was persuaded for XX. Therefore C/D drop

E - use of IT (what does refer to: the apparition OR the destruction); drop
B - use of BEING suggests that Josephus was persuaded when apparition was BEING DESTROYED. But we know the persuasion happened before the destruction.

A