This achievement is a little tougher than the 'Fast Green' Trophy, but still more than doable.
Firstly, save at the beginning of the Act, and then proceed to use another save slot whenever you feel you had a good section, reloading if it went wrong. My fastest time has been around the 1:06 mark (66 seconds) so you do have a little room for errors.
Just keep at it, and maybe keep that save to come back to this if you feel it is beginning to frustrate you.
Video guide to follow
Edit - Video guide added