Public official and small-time land developer lived in Jefferson county, Indiana (1820-1826); later in Fountain County, Indiana.
Entered 320 acres on 4 Sept. 1813 in Section 32 Twp. 5N Range 11E in modern Shelby Twp. He served as a county commissioner, about 1815-1819. He also operated a tavern (in 1815 according to transcribed tax records). Together with David Hillis, later lieutenant governor of Indiana, and John Minor, Wilhite laid out a town to be called Pittsburgh. He also ran unsuccessfully as a candidate for Jefferson County sheriff, coming in a weak third to Thomas T. Stribling, in the summer of 1818.
Achilles received letters from the Indian-Kentucky Baptist Church in 1828. They appear to have moved to Fountain County, Ind., where Achilles, John and George Wilhite are listed in the 1830 census.
William & Mary Quarterly, Ser. 1 Vol 26, p. 248 
The Germanna Record, No. 13 - The Blankenbaker, Weaver, and Wilhoit Families, The Memorial Foundation of the Germanna Colonies, Inc., Publishers, 2006
John Willhoite (1745 - 1837) and His Descendants in Kentucky and Elsewhere. Stroudsburg, VA: Earl and Leona Willhoite
Wilhite/Wilhoit & Allied Descendants of Johann Michael and Anna Maria (Hengsteler) Wilheit 1671-1994 Compiled by Mary F. Mickey
"Kentucky, County Marriages, 1797-1954," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:FW55-HLQ : accessed 8 August 2016), Achilles Wilhite and Polly Hall, 01 May 1794; citing , Woodford, Kentucky, United States, Madison County Courthouse, Richmond; FHL microfilm 252,320.
"United States Census, 1830," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:XHGG-VNZ : 18 August 2015), Eillees Wilhite, Fountain, Indiana, United States; citing 168, NARA microfilm publication M19, (Washington D.C.: National Archives and Records Administration, n.d.), roll 32; FHL microfilm 7,721.
Willhite Family Bible (was in possession of Mrs. Richard Howell, 318 S. Water St, Crawfordsville in the 1980's) 
History of Woodford County, Kentucky by William Edward Railey, Genealogical Publishing Com, 1938 page 327 
It may be possible to confirm family relationships with Achilles by comparing test results with other carriers of his Y-chromosome or his mother's mitochondrial DNA.
Y-chromosome DNA test-takers in his direct paternal line on WikiTree: