Unlocking the achievement is straightforward and is non-missable as it's a story-based achievement: just work your way up the levels cleansing the siphons along the way. After clearing the ground-level ones, if you die those will stay cleansed.
What I do want to highlight, however, is that my progress was blocked at one point in this mission. There's a puzzle on a terminal that you have to interact with to progress and it had no interaction prompt which meant I couldn't open the relevant door (searching online it seems I'm not the only one to encounter this issue). I had to restart the mission from the main menu to get past that part but unfortunately the game doesn't retain your current side mission or personal/weapon mod progress when you do that (it resets you to the state you were at when you first started that mission) meaning I had to re-do all of the side missions I'd done since completing mission 8.
So... in short, I would progress immediately until you reach the puzzle in Dimensional Research to verify that you can proceed before attempting any side missions once mission 9 becomes your main story mission.