Hi @Waqkas-Ahmed
One thing that I'm not seeing anyone mentioning here or asking about is if the mailbox you are looking to get this information for is on prem, or if it's in O365.
You had specified that you are in a hybrid O365 config with Exchange 2010 on prem. In my experience, most organizations that have this setup have the majority of the mailboxes in O365, and the on prem Exchange server is mainly a management box.
If that's the case and the mailbox you are looking to get information on is in O365, then your local Exchange server isn't going to have what you're looking for. You'll want to connect to O365 via PowerShell and use the get-messagetrace command as your starting point, or you can probably just use the O365 Exchange Admin Centre, or Security and Compliance Centre to get the info you're looking for. If you use the Security and Compliance centre you can export the results to CSV, and I believe that you can download a CSV via the Exchange Admin Centre GUI on message traces dealing with items greater than 7 days old as well.
The trace will take a while since you're going back further than 10 days, I generally run it and then grab it the next day. There are some enhanced traces you can do if the default doesn't have what you're looking for. I seem to remember that there is some limit to how far back you can go, but I don't remember exactly what that limit is and I'm having some trouble tracking it down right now, you can definitely do the last 90 days though.
Here's some articles to help you out:
Message trace article from MS: https://docs.microsoft.com/en-us/exchange/monitoring/trace-an-email-message/run-a-message-trace-and-view-results
Using Security and Compliance Centre to do a message trace: https://support.office.com/en-us/article/message-trace-in-the-office-365-security-compliance-center-3e64f99d-ac33-4aba-91c5-9cb4ca476803
Message trace FAQ including all related powershell commands: https://docs.microsoft.com/en-us/exchange/monitoring/trace-an-email-message/message-trace-faq
How to connect to O365 via powershell: https://docs.microsoft.com/en-us/powershell/exchange/exchange-online/connect-to-exchange-online-powershell/connect-to-exchange-online-powershell?view=exchange-ps
Hope this helps you get what you need.