I use mouse steering with my trackball. The only times I missed was when I tried to get cute with throttle settings and all that. It worked much better when I just fired up full impulse and let the Force flow: Relaxed and not trying too hard.
Gym "No. I did not try doing it blind. Get real..." Quirk
Put energy into engines. I think a lot of people having this problem have low engine settings.
Ditto. Switch you power profile to Speed mode. The 3rd Icon on the top of your Ship Power window. And move through the first gate at 1/4 throttle setting. Let the gates speed you up. they don't need help from you.
Personally I found it easier just using the AWSD keys for steering (well the AD keys). In speed mode, line up for level flight for the game and then fly through the fight gate, and then tap the AD keys to adjust my vector to line up for the next game. If your ship is too twitching at Full Engine Power (100), back the Engine Power back down to 75 or 50 to make it less responsive.
I've got a slow machine and couldn't do it using the keyboard, but had no problem once I switched to using the mouse with a "chase camera" view (I didn't know there was any other). My mouse is set fairly sensitive so small mouse movements yield big ship movements. +1 on Full Impulse.
I was seriously outgunned by the final swarm of Klingon ships while trying to destroy the comet. LC7 / Fed Cruiser/ Mark IV everything.. Multiple respawns....deep shame.
I had great luck with putting my engine to .75 impulse and then doing it. I still made it in under the time allotted, and it allowed me better control of my ship. Also, following the blue line is great advice. Give these a try!
I was also very overwhelmed when I first started this mission, I just couldn't seem to hit all of the gates. After reading some of the related threads and advice from some other captains, I was finally able to complete the slingshot.
The two most important things to make it easier are:
1. Zoom in your view so that you are almost right behind your ship.
2. Hit the first gate at just over half impulse speed.
I was then able to use the keys to control the ship enough to hit all the gates.