Include the binary in your Alpine Dockerfile like this:
RUN apk update && apk add --no-cache fontconfig && \
mkdir -p /usr/share && \
cd /usr/share \
&& curl -L https://github.com/Overbryd/docker-phantomjs-alpine/releases/download/2.11/phantomjs-alpine-x86_64.tar.bz2 | tar xj \
&& ln -s /usr/share/phantomjs/phantomjs /usr/bin/phantomjs \
&& phantomjs --version
The only thing that you should install is fontconfig for configuration that comes with the package.
Despite that, the binary release includes all dependencies statically linked to this release. No need for installing additional phantomjs dependencies in your image.
Have a good time and enjoy minifiying your Docker images.