While the walkthrough suggests combining the Elite and speedrun achievements in one run it doesn't include an Elite playthrough in any of the videos so I thought I'd point people towards one. Below is a video guide that I found really useful which allowed me to complete the game in 1:48:33, picking up 8 life and energy cells each along the way to increase survival chances, and of course, not spending a single ability point.
I was also able to get the Immortal achievement during this run by quickly pausing and quitting to the menu as soon as I died (before you respawn), or quitting sooner if it looked like death was imminent. On the 2 occasions I wasn't quick enough (the death counter in the pause menu no longer showed 0 when I loaded back in) I'd load the previous backup by pressing Up when selecting the save file to load up an earlier checkpoint and retrace my steps. Sadly you can't use this method on the One Life difficulty, but it'll work on all other difficulties if you want to go for Immortal outside of a One Life run.
If you're also going for the Supersonic achievement quitting when you die can also help save time if you're dying repeatedly and keep having to return to where you last saved, as the game timer will continue running. Quitting and resuming from the menu resets the timer to what it was when the last save was made before you died. It's not necessary, and as the video shows there's a fair amount of room for error, but it's something to bear in mind if you feel you're taking too long on a particular section.
This is not my video.
Full credit goes to Optinoob.
Feel free to like his video on YouTube if you find it helpful.