I have a generic mp3 ( photo of similar added, no visible screws,
looks like the cover was slipped on ), the battery's lifecycle
is pretty much gone.

It holds a Li-on battery. Is there a way of opening it to change the battery?

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Maybe. Do you see a way of opening it?

Most of these that have no slip-off access covers, or screws to remove the back, can be pried apart, but will probably require one of those plastic prying tools that can help do that without damaging the case. My Palm Pilot was such, as I recall.