It should be doable if you quickly move round through the asteroid fields, you need to take a longer route rather than just heading straight to the top. Remember the star destroyer takes a little while to come in and struggles to hit small ships

i have tried this ~10 times and for the last 3 the star destroyer killed the shuttle within its first 10 shots

Naturally I can't get the Radeon recorder to work again, but I literally did this mission again an hour ago, lot close this time, but the SD was only close enough to take some long range pot shots at it. I'd guess you're either traveling too close to it or you're taking too long to pass through the gap between the SD and lancers. :o

I'll try to get my recorder working and upload it to my google drive with an url for you or anyone else whom needs it.

Used the wrong hotkeys, D'oh! Here ya go, skirted a little too far to the right this time, but still made it (should have had the shuttle go on the left side of the freighter instead of squeezing between that and the station). Still, hope this helps.

Edit : copy the whole url into a browser tab, for some reason clicking it through steam don't work right....
https://drive.google.com/file/d/1oMaoJqC52mYf0rFoVc8IiAtGLVoBbupj/view?usp=sharing

Thanks for the guide Vanguardian ;)