General advice

Here's some general advice about getting fast times. For level-specific advice, see the commentaries to my speed run movies; there's potentially going to be quite a lot you can pick up there, though I'd encourage you to try and develop your own tactics first, as that's part of the fun.

Fine judgement

Obviously you'll want to push hard, but not so hard that the risk of coming a cropper becomes too high. It's a matter of fine judgement that should improve as you make successive attempts and get used to the dangers in each area. I strongly recommend sticking with one difficulty level, so your judgement remains good about how gung-ho you can afford to be. It would be a bad idea to play on Heroic for a while then attempt a speed run on Legendary, for example. You might end up getting killed through underestimating the danger.

Honing your tactics

You'll need to think about each area and how best to tackle it, though in many cases the way you tackle one area can have a significant impact on how you tackle the next, because of the weaponry and ammo you're left with. Hone your tactics and technique. Some situations are relatively chaotic, but in others you can potentially get used to a pattern of action depending on where specific enemies are. When it comes to covie weapons the needler works relatively slowly, which isn't ideal for a speed run, so I wouldn't normally use it. Plasma weapons generally work much faster, and I'd especially recommend the plasma pistol - at least if you're good at rapidly pulsed fire, which is devastating.

Departing shots

Within a given area, such as a room, you can potentially save a few seconds by killing the last of the enemies as you head for the next area, as long as you're confident you can do it. I'm mainly thinking of minor enemies here, Grunts in particular. The pistol is ideal for this.

Monitoring progress

Especially with the longer levels, it's nice if you can check your times along the way, to judge how well you're doing compared to your previous best. That'll help you know whether you need to push harder or whether it's ok to ease off on the risk factor a little. I suppose the ideal thing would be if you've got a buddy with a stopwatch, noting your time at certain points and letting you know how things are going. Luxury! However, you can potentially take care of things yourself just by glancing at a timer at certain points, which is what I usually do.

All-round sound

Playing with headphones (or a surround-sound system, I imagine) is a distinct combat advantage, as you can pick up exactly where sounds are coming from. That's a big help if you plan on wading into a hectic situation with enemies all around you, hoping to clean up quick. If an enemy shoots at you from somewhere, you can potentially turn and fire at the right spot in practically one movement, without even having seen them.