Who was Dhu al-Qarnayn is identified as Darius the First?

Zulqarnain (one with two horns) is most probably Cyrus the Persian conqueror.

It is narrated that during the Prophet Daniel was appointed among Jews. He was the Prophet who at one time, after receiving revelation from God in a dream, announced the coming of a savior of Jews---the one who would release them from the captivity of the Babylonians. In that dream the Prophet Daniel saw this savior as a ram with two horns (Zulqarnain---one with two horns) (Daniel 8:1-4). The two horns metaphorically showed the two kingdoms of Media and Persia united and ram depicting the savior himself showed him to be the conqueror and king of this united kingdom. This king was Cyrus. He was the one who afterwards conquered the Babylonian kingdom and released the Jews from captivity and allowed them to go back to their homeland and build the temple. It was because of these reasons that Jews held him in very high esteem and considered him as their savior as predicted by the Prophet Daniel.

Holy Book Quran too mentions about him as Zul Qarnain.

While few say he was Alexander the Greek conqueror, but it does not comply fully.

Please read the following source for complete details.

Yeah, that's what your mama asked me last night. I'll tell you what I told her - that's an extremely poorly phrased sentence. Your knowledge of grammar is sub-par.