In addition to basic Tetris play, what strategies are critical to winning Tetris DS in tournament play (items on, best 2 out of three)?
In no particular order:
Ability to form T-Spin opportunities between (or instead of) Tetrises; this will let you keep a Back-to-Back chain going if need be
Remembering that you're in it to win it, not score big, so keep your stack at a maintainable level, usually below half the screen
Focus not only on finding great plays, but using garbage to your advantage; it's remarkably easy to turn a row of trash into a T-Spin Double opportunity
Keep your stack even and know when to go into emergency clearing mode. Avoid sharp towers like the plague because the banana peels will ruin your day.
Number 1 is important because if you can T-Spin fast, you can completely ignore Tetrises for garbage-sending. It also helps for #3 when you need to clean up garbage; it's an easy way to get something back.
Two is important because a T-Spin Triple or Tetris back-to-back will send you up six or so rows, which can easily screw you over if you're already high up.
Other than that, just be fast and don't lose your cool.