Playing .mp3/.wav file using AVR ? How
From what I can see, 8 bit AVRs aren't fast enough to play MP3. Instead projects mostly rely on decoder chips. The idea is that the decoder will decode the MP3 in hardware and produce output signal which can be later processed in an amplifier and sent to a speaker.

From what I can see, you'd either need to get a board which can do the decoding for you like this (this one has SD card reader, amplifier and a small speaker too) or this (both use VS1011E decoder) or make your own board which will house the decoder, amplifier, SD card reader and so on. Here you can find a project which explains how to do that and here is one which used AVR Butterfly platform. Both projects have screens and are battery powered from what I can see.