This is the hardest one in the game for a reason. It takes some practice.
I like to think of this level as five parts: 1) The destroyers 2) The forcefield 3) The missile launchers 4)The core and 5) the escape. This mission is best learning the map with the story playthrough, super story playthrough, and then finally trying for it on freeplay after collecting all the canisters. In the tunnel sections inside the death star, keep firing at all times. If you die, I recommend playing through the level a little farther so you will know how to make it through the next part of the level when you make it through on your next attempt.
Section 1: The destroyers
Unlike your previous encounter, the guns on the destroyers cannot be destroyed, so try to approach them from behind to avoid fire. Keep firing ALL THE TIME to take out enemy fighters. You pick up torpedoes by shooting down enemy bombers and collecting the torpedo from them. I like to use the interceptor here for the firepower, but you can also use the y-wing so you can carry around more torpedoes. There are four ships to destroy each with two nodes that must be attacked. Work counterclockwise around the map starting with the ship just to your left as you begin the level. Get two torpedoes and take it down. Get two more torpedoes and take down ship 2. Get two more torpedoes and take down ship 3. Before tackling ship 4, get your health back up to four hearts. There is about a 3 second delay after destroying the ship before the next section loads. Make sure you have 4 hearts of health before taking out that second node.
Section 2: The Forcefield
There will be fighters and interceptors coming at you from ahead and behind. I like the interceptor here for the firepower and maneuverability. DO NOT WASTE HEARTS! If you are at full health, try to avoid picking up hearts you can backtrack and pick them up later. When you intend to go past the torpedo dispenser you should have at least two health (preferably more), backtrack and pick up hearts if you need to. After loading up at the torpedo dispenser, you will come upon two fixed gun emplacements on each side and 3 or 4 torpedo targets on pipes. Take out the gun emplacements while avoiding their fire. You do not need to destroy these torpedo targets, proceed into the next room where you will find a forcefield with two targets on each side of it. If you circle the room while unloading your torpedoes into the targets, you will take less enemy fire. Go back to the torpedo dispenser and pick up two or three more torpedoes and take out the last remaining target. Once you proceed through the tunnel that the forcefield was blocking, the next area will load.
Section 3: The Missile launchers
Proceed to the right to the torpedo dispenser and reload your torpedoes. Proceed north (up) through the tunnel. As always keep your finger locked on the fire button. Picking up any health boosts you need to get back up to 4 hearts. You will get to a room where the path ahead is blocked and you will see a square barricade on either side. When you approach one of these, it will open up and you will be able to attack the missile launcher behind it with your torpedoes. Here's where your ability to circle comes in handy. If you get too far away, the missile launcher will go back behind its cover. Each missile launcher can launch a missile that will track you around the screen. If you fire a torpedo at the first missile launcher as soon as you can and then fire one the other one as soon as you can get a lock on it after destroying the first one, you will be able to proceed down the tunnel before a missile can catch up to you if you've kept circling.
Section 4: The core
Interceptors will attack you to try to keep you from succeeding, but they usually drop hearts when you kill them so you should be able to keep your health up as long as you don't get paralyzed from the EMP pulse from the sections you need to destroy. There are 5 or 6 doors on the wall that hide an EMP unit that will diable you if you get too close and you will watch helplessly as interceptors blow you up. So to attack them safely move your ship down to the core and fire upon the closed door of the EMP you want to kill. Approach slowly and it will open up. Since you're firing on it, you will be able to land a hit on it before it can get all the way out and shock you. Repeat for each of the EMPs. Each EMP will drop a heart so you can replace any hearts that you may have lost while attacking it. There are two torpedoes targets on the west (left) side of the map, you don't need to destroy them to proceed through the level so ignore them. Once all of the EMPs are disabled (there are 1 or 2 on the right side of the tunnel you came in on), the core will be spinning slow enough for you to attack it. You need to shoot the blue part behind the barriers. You can just pick a spot and concentrate your fire and wait for it to open up. Landing a hit will cause the barriers to blast away. Now the core is targetable by your torpedoes if you have any. If you don't have any, you can pick up one of the torpedoes the core sends out one at a time to the north-northwest part of the room (using straight up on the screen as north). Once you have a torpedo target the core. You will be treated to a short cinematic and then the escape section begins.
Section 5: The escape
This is arguably the easiest section, but don't get cocky. I almost threw my controller through the TV when I died 2 seconds from the end because I was flying in circles in (premature) celebration. Keep flying down and keep toward the center of the tunnel. Keep firing and you will remove and obstacles in your way before you can run into them. There are no enemies shooting at you, so fly as straight as possible so your guns can take out obstacles before you reach them. There will be several (3-5) times where the game will load another section, so don't be fooled and think you've made it until you hear the beep of the achievement unlocking. This section is pretty easy if you play a couple failed attempts all the way through so you have an idea of when the turns are.
Best of luck!