To get this achievement, you must complete all 10 levels of Level Star 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 "L /\' Jl > ^) --" in japanese text (I would type the japanese symbols in here, but TA's solution coding only allows romani text).
On my screen, it was the 5th option, after Doubles / 2 player (the second option), Match/Versus (the third option), and Eraser mode (the fourth option).
In this mode, you have to complete ten levels of 'Level Star' mode, which steadily get harder. I suggest trying to build up the gameplay area, and get as many tetrises as you can. The final stage of this mode requires you to get 40 lines in 120 seconds, averaging a line every 3 seconds.