Walking vs. jumping:

Moving through the air is very slightly faster (~2-3% on average) than walking along the ground:

Machine Gun usage:

This may be obvious to some people, but you'd be surprised how many people don't realize this!

Hold jump whenever you're climbing with the Machine Gun. You climb much faster this way because holding the jump button lowers your gravity whenever you're moving up:

(This also applies to Chako skip—you want to be holding jump for the damage-boosts whenever you're not in the inventory.)

By the way, if you just watched the above video and are about to call me out for running out of ammo before reaching the top of Outer Wall, you should know that by holding jump and tapping the fire button, you can climb infinitely high and actually gain ammo while doing so, even without the Turbocharge upgrade: (It'll still be faster than spamming the button and not holding jump)

Egg Corridor? beginning:

Here's a boost jump that anybody should be able to do relatively easily, even if you haven't yet learned any form of machine boosting (which you should also take the time to learn, by the way):

To do it, walk off the first platform, boost onto the next platform, release the jump button after touching the ground and immediately jump again to conserve as much speed as possible. With the Machine Gun, you can then maintain that speed all the way to the end of that section.

(There is a faster machine boost setup for this, as well as many other places in the run that this mechanic can be abused to save lots of time, but that'll have to be for another guide. :) )