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