Here is the full list of all 43 Puyo Puyo Tetris 2 achievements.
Performed a 3-Chain 100 times in completed matches
Popped 10,000 Puyos in completed matches
Cleared 3 different-colored Puyo groups simultaneously in a completed match
Popped 1,000 Puyos in completed matches
Won your first Free Play match
Played all 6 offline modes
Defeated 3 opponents in an Endurance match
Defeated 5 opponents in an Endurance match
Defeated 10 opponents in an Endurance match
Played all 3 Puyo Puyo Challenge modes
Played all 3 Tetris Challenge modes
Completed the main story within Adventure mode and watched the ending
Won your first Puzzle League match
Achieved 50% completion in Adventure mode
Defeated 15 opponents in an Endurance match
Achieved 70% completion in Adventure mode
Won ten Puzzle League matches
Achieved 100% completion in Adventure mode
Performed a 4-Chain 100 times in completed matches
Performed a 5-Chain 100 times in completed matches
Performed a 6-Chain 100 times in completed matches
Performed an All Clear 50 times in completed matches.
Performed an All Clear 100 times in completed matches
Cleared 4 different-colored Puyo groups simultaneously in a completed match
Popped 50,000 Puyos in completed matches
Performed a 7-Chain 150 times in completed matches
Performed an All Clear 150 times in completed matches
Popped 100,000 Puyos in completed matches
Cleared 1,000 Minos in completed matches
Cleared 10,000 Minos in completed matches
Performed a Tetris Line Clear 50 times in completed matches
Performed a Tetris Line Clear 100 times in completed matches
Performed a Back-to-Back 25 times in completed matches
Performed a Back-to-Back 50 times in completed matches
Performed a 5-Combo in a completed match
Performed an 8-Combo in a completed match
Performed a Perfect Clear in a completed match
Performed a Perfect Clear 3 times in completed matches
Cleared 50,000 Minos in completed matches
Performed a Tetris Line Clear 200 times in completed matches
Performed a Back-to-Back 100 times in completed matches
Cleared 100,000 Minos in completed matches
For obtaining all trophies.