Here is the full list of all 43 Puyo Puyo Tetris 2 achievements.
Popped 1,000 Puyos in completed matches
Cleared 1,000 Minos in completed matches
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
Won your first Free Play 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
Popped 10,000 Puyos in completed matches
Performed a 3-Chain 100 times in completed matches
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 3 different-colored Puyo groups simultaneously in a completed match
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 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.