Optional restrictions
You can vary the challenge by imposing restrictions such as limiting yourself to certain weapons, forbidding the use of vehicles, or whatever. I do a lot of that and it gives lots of different and interesting play experiences. You'll potentially need to work out new ways of tackling certain areas effectively, which can be quite enjoyable in itself. It greatly expands the amount of fun on offer with the speed run idea. Here are the main restrictions I've got in mind.
Weapon restrictions
Limit your weapon use to certain weapons, once at least one such weapon becomes safely available. By 'weapon' here I'm talking about hand-held guns, not other offensive equipment (grenades, Shades and vehicle weaponry), which you remain free to use. The limitation only applies to firing, let me add. When it comes to melee, you can be holding whatever you like.
If your initial combo doesn't include any such weapons, the default convention is that the limitation only comes into effect once you're able to safely pick up at least one such noticed weapon. But if you want to make it apply right from the start, forcing you to rely on grenades and melee to begin with, you could always do so of course. I'm not so keen on that 'strict' version myself though, as it takes you well out of the realm of normal combat and tends to lead to frustration.
There's so much potential here. Limiting yourself to covie weapons can be interesting for example, especially if you're more used to working your way through with the all-powerful pistol. Some other ideas are to forbid yourself the long-distance luxury of a sniper rifle, or the power of the rocket launcher (vehicles can be tackled with small-arms fire and grenades instead). Or allow rockets against vehicles only - not against foot troops.
Vehicle restrictions
Limit your use of vehicles in some way. Here are some suggestions, with elaboration so you're clear on what I mean when you see me using any of these standard phrases.
"No vehicles": This means you mustn't board vehicles at all - except that if you do so accidentally when you meant to reload (arrrgh!), that's ok as long as you dismount right away and it doesn't cause a Marine to do any chain-gunning. I often adopt this restriction as I like to focus on foot-based soldiering.
"No splattering": This means no killing enemies via vehicle impact (something which you can potentially use to wipe out whole clusters of enemy fast). This will oblige you to use weaponry or allies instead.
"Vehicles for transport only": This means no splattering and no use of a vehicle's weaponry, including by Marines. But you'll still be able to use a vehicle to reach positions from which to attack on foot, or to let passengers fire personal weapons; so vehicles still have some combat use.
"Vehicles for personal transport only": Like the above except you're also forbidden any passengers. So, vehicles can only be used for getting you (and only you) places.
No medkits
Forbid yourself any medkits. Yep, no magical instant healing for you! Needless to say, you'll have to be far more careful in your battling. You can afford a few slips, but that's about all. If you lose health you'll need to be careful not to accidentally use a medkit, else it's game over (no reverting remember).
Zero health loss
Even more extreme, forbid yourself from ever losing a health bar. We're into perfection challenge territory now, which is bad enough even when you're allowing yourself all the time you need, let along doing it against the clock! Good tactics and clinical technique become of the utmost importance. Definitely not something for the gung-ho merchants.