For this achievement, using the Tie Interceptor, as with many of the other craft based "undefeated" missions, makes it not too bad.
Try to avoid flying in straight lines, I found using zig-zags, circles, figure 8's all work, and use the roll / loop option if you have a bunch on your tail.
Start of by taking out all 16 turrets as quickly as possible, don't worry about taking down anything else unless, you need a heart or two.
The remaining sections all have asteroids that can be destroyed to provide the pink bombs needed to blow up the barriers, and giant asteroid towards the end.
There will also ties on your tail, don't worry too much as both the ties and asteroids can drop hearts, just don't let yourself get swamped. The asteroids will also respawn so don't worry if you still need 1 pink bomb to progress.
You have probably played recently and remember that once you get to an enclosed area with a barrier, you need to go inside the large "crater" to get more pink bombs. (I only add this as it had been a while since i played it last and had forgotten that bit myself).
Compared to the other similar missions, it is one of the easier ones.