Here is the full list of all 58 Square Game achievements.
Clear 10 Level by removing all Blocks
Removed more than 200 Blocks on easy difficulty
Removed more than 100 Blocks on easy difficulty
Clear 5 Level by removing all Blocks
Solve a row and a column with more than 6 blocks each in one move on easy difficulty
Solve a row and a column with more than 6 blocks each in one move an medium difficulty
Solve a row and a column with more than 6 blocks each in one move on hard difficulty
Removed more than 400 Blocks on easy difficulty
Removed more than 800 Blocks on easy difficulty
Removed more than 1,600 Blocks on easy difficulty
Removed more than 3,200 Blocks on easy difficulty
Removed more than 6,400 Blocks on easy difficulty
Removed more than 12,800 Blocks on easy difficulty
Removed more than 25,600 Blocks on easy difficulty
Removed more than 51,200 Blocks on easy difficulty
Removed more than 102,400 Blocks on easy difficulty
Removed more than 100 Blocks on medium difficulty
Removed more than 200 Blocks on medium difficulty
Removed more than 400 Blocks on medium difficulty
Removed more than 800 Blocks on medium difficulty
Removed more than 1,600 Blocks on medium difficulty
Removed more than 3,200 Blocks on medium difficulty
Removed more than 6,400 Blocks on medium difficulty
Removed more than 12,800 Blocks on medium difficulty
Removed more than 25,600 Blocks on medium difficulty
Removed more than 51,200 Blocks on medium difficulty
Removed more than 102,400 Blocks on medium difficulty
Removed more than 100 Blocks on hard difficulty
Removed more than 200 Blocks on hard difficulty
Removed more than 400 Blocks on hard difficulty
Removed more than 800 Blocks on hard difficulty
Removed more than 1,600 Blocks on hard difficulty
Removed more than 3,200 Blocks on hard difficulty
Removed more than 6,400 Blocks on hard difficulty
Removed more than 12,800 Blocks on hard difficulty
Removed more than 25,600 Blocks on hard difficulty
Removed more than 51,200 Blocks on hard difficulty
Removed more than 102,400 Blocks on hard difficulty
Solve a row and a column with more than 5 blocks each in one move on easy difficulty
Solve a row and a column with more than 4 blocks each in one move on easy difficulty
Solve a row and a column with more than 3 blocks each in one move on easy difficulty
Solve a row and a column with more than 5 blocks each in one move on medium difficulty
Solve a row and a column with more than 4 blocks each in one move on medium difficulty
Solve a row and a column with more than 3 blocks each in one move on medium difficulty
Solve a row and a column with more than 5 blocks each in one move on hard difficulty
Solve a row and a column with more than 4 blocks each in one move on hard difficulty
Solve a row and a column with more than 3 blocks each in one move on hard difficulty
Clear 25 Level by removing all Blocks
Clear 50 Level by removing all Blocks
Clear 75 Level by removing all Blocks
Clear 100 Level by removing all Blocks
Clear 150 Level by removing all Blocks
Clear 250 Level by removing all Blocks
Clear 500 Level by removing all Blocks
Clear 750 Level by removing all Blocks
Clear 1,000 Level by removing all Blocks
Clear 1,500 Level by removing all Blocks
Clear 2,000 Level by removing all Blocks