I would guess you have to collect (shoot) those purple morph eye things, on top of just explore the map. If you have 9/10 collected in a level, maybe there's a secret location you haven't found, thus not obtaining the 100% exploration.
This one is much easier than I initially thought. Just go through the game and keep checking the map, if you enter a new area the square on the map lights up bright blue to show you've been there. Do this for every square on every level, it worked for me and I didn't shoot all the morph eyes on that particular run (I had got them on a previous run though).
One heads up, there is a square you can't get to in the generator in the train station level, it doesn't count towards the achievement.
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