Wikipedia
The mystery surrounding the identity of Joiakim is rather convoluted. Biblical texts seem to conflict with one another, as is explained here. In a similar fashion the history of Josephus (Antiq. 11:121) mentions Joiakim, or 'Joacim' but does not include many details regarding his identity or role.
Biblical Citations
-1 Esdras 3:9; 5:5 (Joiakim is referred to as the son of Zerubbabel) The Esdras genealogy of Zerubbabel's sons is considered to be highly confused.
-1 Chronicles 3:19 (Does not mention Joiakim as son of Zerubbabel, and there is no reference to Joiakim's role as a priest of the David line)
- Judith 4:6-7; 4:8; 4:14; 15:8 (Recognizes Joiakim as a High Priest that hold religious and military authority)
-Because there is no evidence that a high priest would exercise such a wide range of powers, some scholars believe that Joiakim may be a pseudonym for a person from either the Hasmonean period, the time of Trajan or Hadrian, or as a "representative figure of the priesthood in general."
- Nehemiah 12:10, 26 However, "this list is artificial and problematic, but its existence reflects the importance of priests and Levites in this period." (Identifies Joiakim as a High Priest, the son of Jeshua)
- Susanna 1:1,4,6,28,29,63 (The book of Susanna states that Joiakim was the husband of Susanna, a very rich man living in Babylon and the most honored Jew of them all, however according to the New Oxford Annotated Bible it appears that this Joiakim is not connected to other Joaikims in the Bible (confirmed by Josephus))
Josephus
-Joiakim may have aided in the rebuilding of the temple, if he was a son of Joshua.
-Joiakim is also labeled as a contemporary of Esdras
-Joiakim and Esdras may even have worked alongside on another, filling the Priestly role; Joiakim is called the "High Priest" while Esdras is referred to as the "Principal Priest of the People".
-Due to the prominent role of Esdras, as evidenced in Ant. 11:120-11:158, theories have been suggested that Esdras actually replaced Joiakim as High Priest.
-Josephus used unknown sources to conclude the following, "And it was his [Ezra's] fate, after being honoured by the people, to die an old man to be buried with great magnificence in Jerusalem. About the same time also died the high priest Joakeimos, whom his son Eliashib succeeded in the high priesthood
-The combination of 1 Esdras and the way Josephus interpreted certain biblical passages, led him to believe Joiakim and Ezra were contemporaries.
-Josephus also took liberties to fill in the gaps between Ezra 6 and 7,"in which one jumps from the reign of Darius I (522-486 BCE) to that of Artaxerxes I (465-424 BCE) by relating the Ezra story to the days of the intervening monarch Xerxes. For this maneuver, he found support in Nehemiah 12, which seems to make Ezra the contemporary of the second high priest Joiakim who very likely served during Xerxes' reign."