Search for and test a web-scraping tool that meets the requirements.
Python is a pretty common choice for scrapers, though there are others.
Automator, not so much.
The other option is integration with the data driving website, if it’s part of your own organization, or if the data can be exported in a format that does not require scraping.
Scraping tends to be precarious, and has a habit of failing when the website changes. Or potentially also if your scraper creates too much load too fast, too.
I’d also start looking for another job too, because this boss is… someone I’ve met before.