For tuning SharePoint performance a good knowledge of multiple Microsoft products is required like:

Microsoft SQL Server: A DBA level knowledge is required for a person tuning SharePoint databases. Typically for performance issues/performance tuning at the database level the DBA needs to check the IOPS (input/output operations per second) on content databases. IOPS requirements for content databases can vary significantly based on:

Then there are other factors such as temp DB size, backup and storage configurations, details on how the underlying network storage is configured and so on. It is necessary for a person tuning SharePoint DB to know how to use the SQL Server Profiler tool for gathering critical performance related information.

Microsoft IIS: This is often an overlooked area when looking for performance issues. A good level of IIS working is required, particularly on:

.Net 4.x: A good knowledge of .Net is required wherever customizations are done using Visual Studio code. Knowledge of the Visual Studio performance analyser and debugging .Net code is required.

Microsoft SharePoint: You need to know your way around in the SharePoint Central Administration Site for finding various aspects of the farm, site collection and sites. For SharePoint performance particularly you need to know:
One non-Microsoft product that I find pretty useful for SharePoint performance tuning is Fiddler. Fiddler is a tool for observing and debugging HTTP traffic between a browser and a web server. SharePoint delivers all its content via HTTP, so Fiddler can tell a ton about how SharePoint responds to users. You can download Fiddler from http://www.fiddler2.com/fiddler2/.

The performance of the system is not a one-time event. It needs to be monitored daily and any unusual spikes in memory need to be timely investigated.