Freelancer Done Quick - hints and partial walk-through
It is important that you have a general plan which ships/equipment you'll be using for each mission, where you'll be getting this equipment, and where the money for this is going to come from. There are not all that many options for levelling up without losing time (the thread Level 7 covers many of them), so you'll probably want to weave your plan around a sequence of these options. I'll sketch my 04:32 h T6 campaign (T-Hawk's mod, 6 battleship kills) later in this post and I think that plan isn't too bad.
The second-most important thing is to focus on the objective: do you want to beat the game quickly, or do you want to maximize your kill stats? For the former it does not matter whether you deliver the killing blow or whether an NPC does that - what matters is that all hostiles get eliminated quickly so that the story can proceeed. So, if a hostile gets out of your firing cone without shield and with mere shreds of hull armour left, let a friendly NPC deal with it and instead bite into the next enemy that has full shield & armour. Of course, this applies only to scenes where progress is triggered by elimination of all hostiles. Find out what the real objective is for each scene and go straight for the jugular (e.g. mission 2 near the NY jumphole: drop out of cruise when you are in gun range of Ashcroft, tractor him in and head for the NY jumpgate, ignoring the other baddies).
Things like flash-docking (i.e., docking without delay) are a must if you want to beat the game really fast, especially the trickier things like docking at the same time as some bleeping NPC that activated the docking ring or jump gate from far away just as you were about to dock, or how to deal with tradelane disruptions quickly. Of course, traders will have this down pat but fighters may have a bit of learning to do here (the best way is to be a trader for a while). Also, don't wait for mission way points to pop up while the NPCs are chatting - when you have done your duty in a scene, activate cruise and go to where the mission will continue when the chatter is over. Case in point: the skirmish at Prison Ship XT-19 during mission 1. When you have blown up the last Rogue, head immediately in the direction of Planet Manhattan (actually, slightly to the right and up if you are aligned with the system plane (space bar)). If you do this right then you will be less than 2 km away from the nav point when it pops into existence after the NPCs are done with their chatter.
Also, if you want to beat some particular scene faster then try to find qualitatively different approaches rather than doing the scene with the same equipment in the same way over and over. Case in point: when I flew mission 1 again for the walk-through I loaded my Starflier with 3 Lavablade Mk I instead of the 3 Justice Mk I that I had used in my T6 run; the much better punch of these weapons enabled me to shave 2 minutes off the time for mission 1, which is quite a lot. Another example: after flying mission 3 for the walk-through I found that I finished it just barely after one hour total time played and I thought it should be possible to beat it before the one-hour time mark. So I played it again but after meeting Walker in space near Planet California Minor I changed course to Willard Station without even dropping out of cruise (when Walker said 'There you are.' or something like that). That way I was only a few km away from Willard instead of 17 km when Juni and Walker were done chatting, and this simple trick shaved more than half a minute from this mission.
Last but not least, remember to sell your nanos/batts and any other capacity-limited potential loot things (ammo, commodities) before going into a mission, lest you find that there are thousands of credits' worth of loot floating in space that you cannot tractor because your capacity is full. Balance capacity for loot against tactical necessities for beating a mission quickly (especially if you want to fry a few cruisers or battleships).