Like most players I failed my first attempt, because I was using the zqsd (azerty... ) keys... And as a result I was overcompensating and kinda surprised by the boosts each gate gives you...
After I failed the first attempt, I went in full impulse and mouse steering my ship... That ship was the free ody btw... Mouse steering is more precise, and less direct then using the keys. Might need a couple of seconds to adjust but when used to it it is pretty usefull; but I dont use the mouse to steer in combat.
To mouse steer hold down BOTH mouse buttons and move your mouse in the direction you'd like to travel. Simple right? Its easy enough...
(it could help though if you ever seen STIV: The Voyage Home...; in there the crew of the BoP which is Kirk, Sulu, Spock, Bones and Scotty fly their commandeered BoP that belonged to Kruge around our very own sun to achieve temporal escape velocity or time travel in other words..., and to be honest that scene gives me goosebumps, each time... xD I dont know why...)
Oh, by the way, this mission is not impossible... ^^
I've done it dozens of time with various ships. It can be more difficult with larger ship's turn rate/helm response stuffed into the little holo ship. I also have had a few issues running it on my clunky old laptop when playing out of town. I've always used the mouse to steer.
In the end, there is always the auto pilot option after you've failed a few passes. Thus, it's never "impossible".
Mouse steering is the way to go. Just follow the blue line. I play this mission a lot, because the klingon disrupter pistol is an awesome ground weapon and I want to have it on all my characters, about 10 in total. I tried it once with keyboard turning and I failed completely.
I do like this mission because it is a nice story, good balance between ground and space combat and can played fast paced, which helps for replayabillity.
The other day I got a funny experience. You have to destroy the comet and you also are attacked by Klingon ships. Then you should try to not alter the timeline, meaning you should not destroy the Klingo leader K'Vat or something.
To be honest, in most of my play throughs I kill/destroy the dude, because I use a lot of AoE abillities to finish of the comet and K'Vat (or what?) keeps fighting you. (It seems you cannot fail this mission, by just altering the timeline. I do not care about this K'Vat and nver failed the mission)
So I decided to use another tactic. I will only attack the comet and destroy it, while not making a scratch to any Klingon vessel. This wasn't difficult since I flew a BoP with battle cloak, so I could attack the comet, cloak, loose aggro from the Klingon ships and make another hit-and-run for the comet.
More and more Klingon ships arrive on the scene, so this was the situation. The partly destroyed comet with the debris pieces, Klingon ships that were lying there inactive, since they had no aggro. K'Vat patrolling and I patrolling to get to an opportunity to hit some comet debris. I was cloaked.
At some moment he came very close and I began to wonder If he could detect me. We weren't on a collision course, but then he wasn't flying in a straight line either. And then he ran into my ship. His ship exploded and was destroyed, I was at 40% hull. I could finish the mission, but again, a time line was distorted.