For this achievement, you have to finish ALL 100 levels.
It's as simple as that.
It doesn't matter what scores you have or however many stars you have. All you have to do is complete the levels' tasks.
If you've having trouble with a task or a level, I recommend getting the colour-cluster hexes (i.e., getting 5 of the same colour in one combination), as that can really help you open up the level a bit, and give you more opportunities to get past a problem section.