Using the Jenkins CLI - console - command
java -jar jenkins-cli.jar console JOB [BUILD] [-f] [-n N]
Produces the console output of a specific build to stdout, as if you are doing 'cat build.log'
JOB: Name of the job
BUILD: Build number or permalink to point to the build. Defaults to the last build
-f: If the build is in progress, append console output as it comes, like tail -f
-n N: Display the last N lines.
E.g.
ssh -l <ssh_username> -p <port_no> <Jenkins_URL> console <JOB_NAME>