how can I get my iPhone 4s battery replaced?

Try here: iPhone Battery Replacement - Official Apple Support

I'm not sure if Apple actually replaces 4s batteries any more.

I still have a 4s listed as one of my devices. I can't do any online service requests for it any more to get an approximate price. I get this message:

Online Repair Unavailable

We’re sorry, but online repair isn’t available for this product. Please choose another product or contact AppleCare.

I'm not 100% sure how Apple does battery replacements for the 4s. I don't believe they've ever taken any in, replaced the battery, then handed the same device back. I believe they've always done it as a complete replacement where the customer is responsible for for having a working backup.