If you wanted to knock this one out really quickly you could do a survival game and kill a few enemies and then let your core die. It seems this specifically means the ship you control.
A more focused approach in a mission would be to make sure you use cover and dodge. When you use the charge beam you get a small shield in front of you until you fire (holding down the trigger). If you're struggling with any boss missions (the first one for example) wait for a mission with no bosses and you should just be able to back off when you've taken too much damage.
You could also make sure you play on the lowest difficulty to get this with no issues.