If you're a good player (or you have used the guides to complete the game), you would have turned around 600 - 700 Hexagons upon completion. To get the remaining amount and unlock the "1000 Turns" achievement, the easiest level to farm is Level 4.20.

This level may not have the most number of tiles to turn, but you only have to turn the hexagons in two straight lines, so it is the easiest and quickest to complete. Just turn two tiles as depicted below to pull the triangle to the bottom, then block the bottom and turn all the tiles above, and once the triangle comes to the other side, repeat again. Simple.


NOTE: Make sure you complete the level. If you refresh the game before completion, the "tiles turned" will not be counted!

After you complete the level, the game will automatically go to Level 4.21. Click "back" to go to main menu again, click "4.20" and then repeat this process until you unlock the achievement. Every time you complete this level, you get 18 tiles, so you'll turn almost 100 tiles in 5 attempts (which will take around 2 minutes) and you'll get this achievement in no time. Hope that helps.