Here is the full list of all 15 Tetra Online achievements.
Perform a total of 500 T-Spins (Singles, Double or Triples)
Achieve a 40L time under 1 minute
Achieve a 40L time under 45 seconds
Achieve a 40L time under 30 seconds
Reach a total of 10,000 total line clears
Achieve at least 1 win in Puzzle Duel
Reach a total of 100 wins in Puzzle Duel
Reach a total of 2,000 wins in Puzzle Duel
Reach at least 20,000 of rating in Puzzle Duel
Perform 3 Perfect Clears in a row
Perform a total of 1,000 Tetras
Perform a Mini T-Spin Double
Have an opponent leave during a match
Perform a 20 combo
Perform a Secret Grade