This isn't as hard as it seems, just kill every enemy in all five archives. Using a controller will make this much easier.
Practice all five levels, learn where the enemies are.
The small enemies (they kinda look like minnows) that are in massive groups do not count towards your purification, so you do not have to worry about them. Hooray!
If you are just going for 100% purification, then hold down the right trigger and spam the A button. This will make your attacks much more faster.
If you are having trouble with a certain archive, consult with the guides on their particular achievements.
These are listed here:
The Genius Play achievement in Child of Eden worth 172 pointsClear the Matrix Archive on Normal Difficulty Mode and achieve 100% purification.
You will grab all of those achievements along with the ones that are obtained with just beating the archive, if you haven't beaten the game already.
That is obtained by getting 100% purification on the Hard difficulty mode, which should be easier after already doing them on normal.