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