Here is the full list of all 34 PEG achievements. It takes around 6-8 hours to unlock all of the achievements on Windows.
Clear all CROSS levels.
Obtain all achievements.
Clear 30 daily levels total.
Move 3000 PEG pieces.
Clear 20 daily levels total.
Move 2500 PEG pieces.
Clear a CROSS level.
Clear all HEXAGON levels.
Clear 10 daily levels total.
Unlock the CROSS board.
Move 2000 PEG pieces.
Clear a daily level.
Clear all DOUBLE DIAMOND levels.
Unlock daily levels.
Move 1500 PEG pieces.
Clear an HEXAGON level.
Unlock the HEXAGON board.
Clear all CIRCLE levels.
Move 1000 PEG pieces.
Clear a DOUBLE DIAMOND level.
Unlock the DOUBLE DIAMOND board.
Beat the 7th CIRCLE level while only moving the red PEG piece ONCE.
Move 500 PEG pieces.
Clear all SQUARE board levels.
Clear a CIRCLE level.
Unlock the CIRCLE board.
Clear a SQUARE level.
Clear all STAR board levels.
Unlock the SQUARE board.
Clear a STAR board level.
Clear all TRIANGLE board levels.
Unlock the STAR board.
Clear a TRIANGLE level.
Complete the tutorial.