Here is the full list of all 19 Quatris achievements.
Clear two rows at once.
Clear three rows at once.
Clear four rows at once.
Clear three rows at once on Hard.
Get your first spot in the local highscores.
Get a #1 in the local highscores.
Get a spot in each of the 6 local highscores.
Get #1 in each of the 6 local highscores.
Have 10+ blues on screen, but no oranges.
Have 10+ oranges on screen, but no blues.
Have 200+ blocks on screen.
Clear 1000 rows over the course of your career