I recently worked through the single missions including this one and tried a rather unconventional approach. It worked as I earned all 1000 points and was not fired upon with a torpedo
At the start, I sprinted south for a short while to get farther away from the helos. Using ESM bearings, I then fired 4 harpoons interpersed with 4 tomahawks. I figured 2 or 3 of the harpoons would hit surface ships (SAMs would take out the rest), and maybe cripple the carrier. The tomahawks made good decoys for the SAMs.
After the missle fire, I again went deep and sprinted around the backside (western side) of the surface force. Then I took out the remaining surface ships.
Finally, I continued east and tracked the Akulas so I could attack them and finish the mission.
Probably not a good real life strategy, but it worked in this scenario.