Linux Mint has OpenJDK 7 available in the default repos, but not 8 for some reason. You have a couple of options:
To install OpenJDK 8 from a restricted PPA (instructions from here):
sudo apt-add-repository ppa:openjdk-r/ppa sudo apt-get update sudo apt-get install openjdk-8-jdk
Or you can install Oracle Java 8, downloading the .far file from here:
http://www.oracle.com/technetwork/java/javase/downloads/jdk8-downloads-2133151.html
gunzip, tar xvf and then move the jdk1.8.0_xxx dir somewhere like /opt/java, and then (from instructions here):
sudo update-alternatives --install "/usr/bin/java" "java" "/opt/java/jdk1.8.0_102/bin/java" 1 sudo update-alternatives --set java /opt/java/jdk1.8.0_102/bin/java