You can replace it with an aftermarket battery. That takes opening the case and a bunch of fiddling around inside .. If you are good with tools and have a lot of patience then go for it .. look at ifixit.com or iphone4parts.com for the stuff needed .. Otherwise .. Get an external battery case like a mophie or find a local iphone repair place and pay them to do it for you..
Links:
iFixit The free repair manual iFixit
iPhone4Parts Custom Aftermarket Parts for iPhone and iPad
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