If you're naturally good at Tetris, this should be relatively easy to obtain.
If you're still learning or new to the game though, this can be a little tricky. Here's a couple of tips from my experiences:
Just be sure not to worry too much if you mis-place a few blocks here and there leaving the empty block or two, it is quite common with the sharp changes of speed on mis-drops in Expert mode.
Also bank some zone and use it if you're about 3/4 near the top and in a sticky situation, then try to clear as many lines using the zone mechanic before it expires, hopefully giving you a more friendly playfield.
With the time it takes, it depends on how fast your reflexes are. It took me about 80-90 minutes to finish w/ 1 restart (top out) & using the zone mechanic on each stage.
There's no penalty if you top out, you can simply keep restarting until you've cleared the stage or area. You'll still be where you were, only thing is the progress in the stage itself is reset.