In a nutshell:
If you don’t have "Media Go" from Sony (The full program is free), download and install it: Introduction – Media Go – Sony Network Entertainment (http://mediago.sony.com/enu/introduction/)
Put your .aa3 files into a single folder and open Media go. When Media Go has opened, right click on "Music" and click on "Manage Library Folders" and import the folder you created.
After the files have been imported, drag and drop them to a connected storage device. This can be a PSP, a USB, or in some cases, a portable hard drive (you can find connected storage on the left panel). Wait, then you’re done.
Media Go will export the files to the removable storage as a .mp3 file and then you can use the .mp3’s on anything instead of Sony only devices. It might not be the most efficient method, but it can batch export them with little hassle to you. If anyone else has better methods, they should post them here where everyone else can see it too. Personally, I’d prefer something like a plugin for Audacity.
ffmpeg -i input.aa3 output.mp3