See https://github.com/google/google-java-format#eclipse
Before building the plugin, make sure to run mvn tycho-versions:update-eclipse-metadata to update the bundle version in META-INF/MANIFEST.MF.
Run mvn clean package in the eclipse_plugin directory. This will first copy the dependencies of the plugin to eclipse_plugin/lib/ and then triggers the tycho build that uses these dependencies (as declared in build.properties) for the actual Eclipse plugin build.
If you also want to add the build artifact to the local maven repository, you can use mvn clean install -Dtycho.localArtifacts=ignore instead. Note, however, that you then must use this build command for every build with that specific version number until you clear the build artifact (or the p2-local-metadata.properties) from your local repository. Otherwise, you might run into issues caused by the build using an outdated build artifact created by a previous build instead of re-building the plugin. More information on this issue is given in this thread and this bug tracker entry.
You can find the built plugin in eclipse_plugin/target/google-java-format-eclipse-plugin-<version>.jar
With the current build setup, the Eclipse plugin build pulls the needed build artifacts of the google java format core from the maven repository and copies it into the eclipse_plugin/lib/ directory.
If you instead want to build against a local (snapshot) build of the core which is not available in a maven repository (local or otherwise), you will have to place the appropriate version into the eclipse_plugin/lib/ directory yourself before the build.