how to check web navigation/sharepoint perfs for distant user

Customer's Users are complaining about low performance on SharePoint 2013 site. I would like to send a little software or script (I know PowerShell) or even built-in features (like Dev console on IE), to "record" their session on SharePoint.

Then I need to gather a kind of log file, to analyse what is going wrong (too much images downloading ? too slow internet connection ? files are taking too long to open ?).

I'm only talking about one SharePoint site and a known url.

And on the server side, SharePoint is looking good for me (except BLOB cache that is disabled, but atm, not sure it is needed), and same for the SQL server.

Hope I'm clear and understandable enough. TIA

P.S : I'm currently not aware about how users get connected to the SharePoint site, waiting for the customer answer.