There are multiple tricks to getting the Speedster achievement:
- play as fast as you can, right from the start
- don't use infinite spin, it wastes time
- build as many tetrises as humanly possible
- use your hold queue! when a piece falls to the bottom, you can swap it out for the piece on hold, removing a possible mistake and getting a whole new drop - I haven't managed to do it in under 20 without the hold queue.
Because of the hold queue, this achievement is actually pretty easy. Just practice until you're comfortable with going as fast as possible, and you'll have it in no time.