This summarizes the existing translations as far as I know.
For information about the Samguk Sagi, please see the excellent intro at:
1-5 - None available
6-7 - Jamieson, John Charles. “The Samguk sagi and the Unification Wars.” Ph.D. dissertation, University of California, Berkeley, 1969
8 - Samguk Sagi Translation Project, University of Hawaii (Samguk Sagi translation project)
9 - 12 - No translation
13 - Gardiner, Kenneth H.J. "Legends of Koguryǒ (I): Samguk sagi, Annals of Koguryǒ." Korea Journal, 22 (1) (January 1982): 60-69. [part one], "Legends of Koguryǒ (II)." Korea Journal, 22 (2) (February 1982): 31-48. [part two]
14 - 18 - None available
19 - 21 - University of Hawaii
22 - University of Hawaii (in progress)
23 - 28 - Best, Jonathan. A History of the Early Korean Kingdom of Paekche [Baekje], together with an annotated translation of The Paekche Annals of the Samguk sagi. [A complete translation of the Baekje bongi]. Harvard East Asian Monographs, 2007.
The remaining scrolls are chronological tables, treatises, and biographies — 11 of the biographies have been done by Jamieson, but I think the rest are untranslated as well.