Having intimate acquaintance or personal knowledge.
The Century Dictionary (Public Domain)
Use "well-acquainted" in a sentence
"He was young, fluent in English, well-acquainted with Western culture and with the discontent of young Muslims there."
"Adams was well-acquainted with the liberty spawned by monarchy."
"The unusual early burst of demand is partly attributable to the fact that this has been an on-again, off-again deal for such along time that investors are well-acquainted with the company, making it possible for them to decide to buy even before AIA management goes on tour to drum up interest."