Speed Up Magento Website -- 2

Hi, We are running a Magento website which is hosted in Amazon. The loading speed is acceptable but we would like to speed it up further. Actually we have used Google's Pagespeed Insights and Y2Slow to check the site. Besides the size of images which we can handle, there are a few items, which are programming related such as editing some files, we do not want to touch on by ourselves. For this part, we do need a professional to help us to handle it. Then, can we fix our target like working out the outstanding items mentioned by Pagespeed except photo resizing? You may run a simple test at first so that you can more or less understand what we want to complete.