Here is the full list of all 42 Puyo Puyo Tetris achievements.
Popped 100,000
Popped 50,000
Won ten Puzzle League matches
Performed an All Clear 150 times in completed matches
Performed a 7-Chain 150 times in completed matches
Performed an All Clear 100 times in completed matches
Performed a 6-Chain 100 times in completed matches
Played all 5 Arcade modes
Played all 3 Puyo Puyo Challenge modes
Cleared 4 different-colored
Played all 3 Tetris Challenge modes
Cleared 100,000
Defeated 10 opponents in an Endurance match
Defeated 15 opponents in an Endurance match
Defeated 3 opponents in an Endurance match
Defeated 5 opponents in an Endurance match
Clear 200
Cleared 50,000
Won your first Puzzle League match
Performed a Back-to-back 100 times in competed matches
Performed a 5-Chain 100 times in completed matches
Clear 100
Popped 10,000
Won your first Free Play match
Performed a 4-Chain 100 times in completed matches
Performed an All Clear 50 times in completed matches
Clear 50
Performed a Back-to-back 50 times in competed matches
8-Combo
100% adventure mode
Complete Adventure
Performed a 3-Chain 100 times in completed matches
Cleared 10,000
Performed a Back-to-back 25 times in competed matches
70% adventure mode
50% adventure mode
Cleared 3 different-colored
Popped 1,000
5-Combo
perfect clear 3 times
Cleared 1,000
perfect clear