People with large holdings are required to file with the SEC and you can search those records online going back to the mid 1980s.
Someone could download a dump of the whole thing (the SEC has a link and updates it every night) and assemble all of the various documents in a way to get a decent estimate.
An example Form 4 (which will show cost basis of acquisitions):
https://www.sec.gov/Archives/edgar/data/1045810/000104581025...
An example Form 144 (which would give you a pretty good guess as to which shares are being sold; you can then correlate with a known Form 4):
https://www.sec.gov/Archives/edgar/data/1045810/000192109425...