Most versions of this game are welcome for usage with differences being loading times of levels and gameplay lag in the ps2 and xbox versions as far as we know don't affect level times, preferred version is gamecube v1.00 (Non-Player's Choice version) or xbox v1.00 (Non-Platinum Hits version) for the purpose of Explosion Boosting and Explosion Jumping which can be differentiated between.
Alledgedly using specific control schemes helps for more effective controlling through each level, generally recommended is control setup 3 for Gamecube and Playstation 2 while control setup 2 for Xbox, generally it's personal choice as I doubt any control scheme will help improve a level run better than what one's preference and comfort with control schemes is.
Movement diagonally doesn't change speed much at all, but strafing sideways with a little bit of an angle for forward movement in some areas is somewhat effective, running in any direction in general seems to maintain the same speed but this method helps maintain consistency in a run.
In some parts of the level by actually turning when going around corners seems to give better traction of speed, even after running one direction without turning you can run the next direction and re-adjust to get a little speed.
Your own play style comes first
Don't be influenced too much by online information about how to control better or move faster that it affects your play style, get your own personal feel of movement and work out the most effective way to play and move for yourself.
You can get stuck against some walls and parts when moving, the best strategy is to maintain consistent movement, so when moving near walls try not to move too close to the walls, running near walls can allow for better cornering but can mess up a level speedrun quite easily, notably getting semi-stuck for a moment in the bad diplomacy elevator doors invisible wall barriers can really mess things up.
Stairs and Slopes
Maintaining speed is a must, so running straight at stairs and slopes and jumping at them allows to get up them more quickly than just running up them, remember you need the room to run directly at them and jump, if there isn't any room then simply straf or run up normally, sometimes a second jump can be performed directly after the first jump up the stairs, hopefully if it retains speed it'll be more effective, but may not be in some cases, also like with the walls especially avoid walls on stairs and slopes as they can mess up a perfectly good run.
Buttons and Switches
Most buttons and switches you can just hold the action button while approaching them, this allows to trigger them without rapidly pressing the action button, remember this doesn't work with gadget uses and some buttons and switches simply won't work with this method at all, so worth playing and testing the level before speedrunning it, practice each level as in some levels when you approach some buttons you can just hold that button and then the next button may require mashing that action button excessively to activate whatever it activates.
Quick use of gadgets
Something worth mention when doing time records is the quick use of gadgets, using the q-claw on the claw duct and the q-laser on the locks is the main reason to practice for using quick usage of gadgets, either while moving which seems harder or at a certain distance to stop for a moment and quick aim the gadget at what you're using it on, this helps a lot more than just general practice as in the heat of the moment accuracy and partial assumption can be very useful for using gadgets quickly, hopefully it takes less retries.
Accuracy and tough enemies
In some levels and even higher difficulties it is imperative to be as accurate as possible, especially with harder difficulties which head shots may be required or the use of more powerful weapons, maybe shooting from a distance to avoid taking damage faster still requires accuracy, take advantage of rapid fire and powerful guns to take down enemies quicker if necessary, remember on higher difficulties auto-aim can be fairly useful except for headshots, keep a distance from some enemies on higher difficulties as their shots can do some really considerable damage fairly quickly.
Before entering some cutscenes if you're switching guns or gadgets or even using a gadget it'll display that first before allowing the cutscene to trigger, this is only small but can still be time wasting in full game speedruns, worth noting to say the very least, also worth noting is that some cutscenes don't activate on higher difficulties, but with individual difficulty runs this info about cutscenes on higher difficulties might simply not matter.
Explosion Physics - Boosting and Jumping
As mentioned earlier about different versions is that the boosting only works in some specific versions notably the first released v1.00 of 2 consoles, on Gamecube Non-Player's Choice and Xbox Non-Platinum Hits, though some charts may seperate this which is cool, explosion techniques require being airborne during an explosion and somewhat moving away from it at the same time, so if you're jumping up while below the explosion it should throw you up, and it can blast you across longish areas, explosion physics work great despite doing some damage to your health, high jump skips and long areas are still scarce in this game especially long areas, so some techniques aren't used very often.