Q:

Why there's no Targum on Prophets and Writings (נ"ך)?

Allegedly, the Targum on the Torah (Onkelos) was given at Sinai together with the Torah (Meggilah 3a). 
The Prophets and the Writings were written by the Sages with "Ruach Hakodesh". 
Were they given with their Targum alongside the main text, or there was no original Targum for NaC"H, and why Onkelos didn't translate them?

A:

Megillah 3a:

וא"ר ירמיה ואיתימא רבי חייא בר אבא תרגום של תורה אונקלוס הגר אמרו מפי ר' אליעזר ור' יהושע תרגום של נביאים יונתן בן עוזיאל אמרו מפי חגי זכריה ומלאכי...ועוד ביקש לגלות תרגום של כתובים יצתה בת קול ואמרה לו דייך מ"ט משום דאית ביה קץ משיח...ותרגום של תורה אונקלוס הגר אמרו...שכחום וחזרו ויסדום‏
Rabbi Yirmeya said, and some say that it was Rabbi Ḥiyya bar Abba who said: The Aramaic translation of the Torah was composed by Onkelos the convert based on the teachings of Rabbi Eliezer and Rabbi Yehoshua. The Aramaic translation of the Prophets was composed by Yonatan ben Uzziel based on a tradition going back to the last prophets, Haggai, Zechariah, and Malachi ... And [Yonatan ben Uzziel] also sought to reveal a translation of the Writings, but a Divine Voice emerged and said to him: It is enough for you [that you translated the Prophets]. What is the reason? Because it has in it a revelation of the end, when the Messiah will arrive .. .Was the translation of the Torah really composed by Onkelos the convert? ... The ancient Aramaic translation was forgotten and then Onkelos came and reestablished it.

So it seems that there was an ancient tradition of a translation of the Nevi'im, going back to the times of the final prophets at the start of the Second Temple period.
As for why Onkelos did not translate the Nevi'im, Maharsha ad loc. notes that chronologically Yonatan ben Uziel came before Onkelos, so his translation of Nevi'im already existed when Onkelos was translating (or rediscovering the translation of) the Torah.

