To get this achievement, you must complete all 10 levels of Eraser mode in Offline mode.
This game mode unlocks after you get the following achievement:
After this game mode has been unlocked, go to the main menu. Click the first option.
If you have unlocked multiple game modes, this may be a different option, but you want to select the option that looks like "T L T H --" in japanese text. Note that the right side of the 'H' goes down and forms a J shape, as if the letters H and J have been molded together (I would type the japanese symbols in here, but TA's solution coding only allows romani text).
On my screen, it was the 4th option, after Doubles / 2 player (the second option) and Match/Versus (the third option).
In this mode, you have to complete ten levels of 'Eraser' mode, which steadily get harder. I suggest trying to build up the gameplay area, by leaving 4x1 spaces as you go up, so after you erase some of the higher lines, it's much easier to bring the gameplay area back down to the bottom, if required.