I went through all of the Dark Fragments levels from the start until finding one that had a lot of space to work with. I managed to get this achievement on level 21. On this one, you have 6 rows of hexes at the top of the screen, with 5 rows of 'decryptions' hexes at the bottom. This should give you plenty of room to play out the 24 moves you need to to get this achievement. Try to stick to 3-hex clusters so that you do not make any line-clear or colour-clear hexes by doing 4-hex and 5-hex clusters respectively.
You CAN remove decryptions.
You CANNOT remove the Dark Fragments.
Edit: Some players are saying that Level 31 is easier. I never really tried it on that so I can't vouch for that, as I had no problems with Level 21. However, if anyone's having trouble with 21, try 31.