You have to clear the fourth Tetris Road for this achievement.
To get to this, on the main menu:
2nd option (Xbox Live)
3rd option (Create a Session)
Top left option, set it to the 2nd option from the top, which is Tetris Road.
Then select the top most option. This will search, come to a miniature lobby, and then load the game with a 15 second countdown.
To play this mode, you must have completed the previous Tetris road, which means you will have the following achievement:
Scroll down the Tetris Road list to the fourth option (Star Road).
You have 10 stages in this road:
1) Tetris - Get 5 tetrises in 2 minutes
2) Eraser - Erase 4 lines in 2 minutes
3) Target - Remove 3 rounds of target squares in 90 seconds.
4) Cycle - Get a Single, Double, Triple, & a Tetris in any order, in 90 seconds
5) Level Star - Get 40 lines in 2 minutes 10 seconds
6) Big - Get 20 lines in 90 seconds
7) Target - Remove 3 rounds of target squares in 2 minutes 10 seconds
8) Eraser - Remove 6 lines in 2 minutes
9) Cycle - Get a Single, Double, Triple, & a Tetris in any order, in 90 seconds
10) High Speed 2 - Get 10 lines in 40 seconds. Try and finish this stage with a double-line clear, as this will allow you to play the EX stage...
If you complete these, you'll get this achievement, HOWEVER, there is one more achievement you can get in this road...Note: If you fail the EX stage, and you haven't got the achievement, the achievement for completing the road will not unlock, and you'll have to do it again.
If you finish Stage 5 (Level Star) or Stage 10 (High Speed 2) with a double line clear, you'll get the EX stage...
EX) High Speed 2 - Get 35 lines in 2 minutes.
If you manage to complete the EX stage, you get the following achievement: