This game has some tricks that aren't very difficult to achieve no matter how much you have practiced it. These can be done on PC or console.

Sidestep Boost: Hold left in the direction you want to go and then jump! As soon as you jump, turn back to the direction you were facing and you'll find that you are instantly at full running speed, in contrast to the 7-10 second lead up from nothing to full sprint. This saves significant time and once you get the habit of doing it, it becomes second nature. Here's a fun test though: once you get used to this for a few months, try playing the game without it and notice how uncomfortable you'll be. Best place to practice this is at the beginning of New Eden where you have very long straightaways.

Wallrun Boost: Whenever you are near a wall, wallrunning on it, facing it as much as you can without jumping AT it, and quickly jumping off gains significant speed. This can be used to bring you to running speed and give you slight boost. Best place to practice this is in the subway station of New Eden, even if there are guards there.

Ventkick: Likely the easiest of all of these, you simply kick when falling straight down which usually happens when falling out of a vent but can also be done a few different ways, most notably through the Drop-Roll technique. This kick resets the height you can fall down at. You'll still take damage but it doesn't slow down your momentum which is important. To practice this, find a vent somewhere in the game, it doesn't really matter.

"Almost the" Kickglitch: I prefer to call it a Halfglitch and here's why: unlike a kickglitch, you don't jump off of the invisible platform below. This can save a few seconds or so throughout the run. When you kick off of a wallrun, you end up falling (as you could imagine) but then you land on this invisible platform for a few frames. This resets your height and allows you to fall further distances, similar to a vent kick. Best place to practice this is at the very beginning of New Eden against the wall to your right.

Drop-Roll: Likely the hardest one of all of these, a Drop-Roll consist of a player rolling on one surface so closely to the edge that they fall off of it after the rolling animation is complete. This resets the players drop height and can allow them to fall a significantly larger distance than usual. The best place to practice this is at the very beginning of The Boat with the vents to the left. At this spot, you can also practice the Ventkick to prevent having to roll after landing on the blue overhang below.

Hope this helps, but if it doesn't (or if you're looking for harder techniques), here are some more links that may be able to help you out. http://mirrorsedge.wikia.com/wiki/Speedrunning https://kb.speeddemosarchive.com/Mirror%27s_Edge https://docs.google.com/spreadsheets/d/191kBz6cDWKaUvTwv8sxfgJAU_l03D7-E6J7IhW89RzM/edit#gid=0