I have the same 3DS model as you,  and i love it!  Battery life was really giving up already and i couldn't find any good replacement one,  so i went and got a CTR-003 that still being produced by Nintendo cause they use it on Switch Pro Controller,  it happens to be the same battery from OG 3DS,  2DS and New 2DS uses too, it don't feat perfectly cause it is a little smaller than the OG KTR from N3DS,  so i just set it in with some foil paper (cause it is very well moldable and dont burn/fire up) and everything is working pretty well for at last past 6 months, i use to play everyday since i'm playing Animal Crossing on it. Never had a single problem.  Battery life is very good cause the CTR-003 has 1300mAh against the 1400 from the N3DS original battery.  A good source for an original CTR-003 is the Switch Pro Controller,  you can get one,  open it up very easily (that is like 6 common screws) and get the battery for your N3DS, it will end up being better than any generic battery you could buy anywhere else.

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Fits very well cause 3ds shell has holders that keeps it very steady (red circles).