What brand/model is it? If I can look at a photo of another one I can get an idea of what you are having trouble with.
On my phone, the battery compartment cover just slides off with a little thumb pressure and the battery lifts out.
If I can see what you are dealing with, I can be more helpful.
In the meantime, do you happen to have an eyeglasses repair kit? If so, one of the tiny screwdrivers that come with it might work.