There are many ways to go about killing the Destroyer but the most effective, and easiest method I have found is using a Revolver, strafing in the middle between the pillars and constantly shooting it's eye. This will cause critical damage most of the time. Ignore shooting any other part of it's body as the more damage you do to the Destroyer, the more it will "shift," causing it to grow more tentacles or retract them rather than attacking you. With this method, you should be able to take the Destroyer down in less than 5 minutes.
Happy Hunting :)