Are the reports being delivered using Report Manager, SharePoint or a ReportViewer control in a web page?
You're using SQL Server 2008 R2, so the only supported browsers are Internet Explorer, Firefox and Safari and although it doesn't explicitly state it this almost certainly refers to the desktop versions of these browsers so there's no guarantee that mobile versions will work the same way.
So the SSRS technology you are using is not designed with modern day mobile devices in mind. That said you can still try to make this work: You need to ensure the users are using either Firefox (on Android) or Safari (on iOS). Note that Chrome (or related browsers) are not supported at all. You need to consider how the report security is going to work (e.g. only Basic authentication is supported with Safari).
In terms of layout and report components, you'll have to do some trial and error testing to see what works - and remember it may not work on all devices. You might want to consider providing links to render the reports as PDF files, which have much better support on most devices. There is a great blog post by Adam Aspin on some layout techniques for reports on mobile devices here: https://www.simple-talk.com/sql/reporting-services/mobile-bi-with-sql-server-reporting-services/
Generally though, if you're trying to design a solution for mobile devices you really want to consider an upgrade to a more recent version of SQL Server which has support for more browsers (including Chrome) and security options.