This achievement is about 85% luck and the rest is common sense.
The three main rules I would give you are...
1) Try and keep your reserve space free as long as you can. This, in a way, is a second chance to get the piece you need instead of something which ruins your masterpiece.
2) If you have to use your reserve space, try and keep the Z-shaped pieces out of it as everything else can be used to complete your matrix.
3) Count!
Sounds strange but it really helps instead of fighting a lost battle.
a) Count your line level. I always stack a line shaped piece on the side of the matrix as not only is that the easiest place to use the line but you can see if you can still beat the achievement! if you keep the pieces below the line, you can still beat this. If not, then stack another line shaped piece on top of your existing one and start again.
b) Count the units. Always start on the slowest speed first. Don't make things difficult for yourself! This way, as pieces are dropping, you can see where to place the piece and, more importantly, count the units remaining if you were to place it there. For example, if you were about to place a piece but saw it would only give you two units of space left on your right side then you should reconsider as no piece would fit there!
Try not to get frustrated and reset the game constantly if you can't do it within the first 4 lines of the game! After about 20 attempts I managed to do it on the 16th line via a double tetris.
If you find your stacking up then you've got good reason to reset the game.
And remember that even when you get the one perfect gap shape left, it's a 1 in 7 chance that your piece will be next so you MUST be patient!
Other than that, good luck. You'll need it!