Instructions
Blow up every node guarding the core along the walls. Be sure to not get too close; otherwise, you will bounce off and may crash the Millennium Falcon.
Blast the blue casing of the core when exposed.
Shoot a torpedo into the core once the blue casing is gone. Fly carefully, as you will have to travel through every area you flew through in the Death Star (areas 1-4). Be sure to keep shooting the debris that flies in front of you before it hits you. If you do this, you will make it out of the Death Star unharmed.