Historical data for AdSense payments will be available till June 30, 2015. Google gives you an option to export the data in to .CSV format. Once you export into .CSV format, you can open it in MS Excel format and then export it to various other formats.
Another option is, you can go to the historical payment reports using Google Chrome browser and then use the "Print" option. When you print from Google Chrome browser, you have an option to save into a PDF file. This will help you save your AdSense payment report into a PDF file.
Unfortunately, there is no way to save all the details like Payment Type , Payment Date, Payment Number, Tracking Number, cheque clearance date etc. I wish Google had provided some ways to save those details as well.
When you visit the payment history in AdSense dashboard, you can click on the link to see details of the payment and tracking information. Unfortunately, there is no option to save those details in bulk. Your only option is to open the details page one by one and save it.