Here is the full list of all 19 Puzzler achievements.
Complete all the levels
Complete the first level, which has the figure "Ychar_corner"
Complete the first level, which has the figure "2char_corner"
Complete the first level, which has the figure "Zigzag_corner"
Complete the first special level
Complete the first level, which has the figure "Bident_corner"
Complete the first level, which has the figure "M_char"
Complete the first level, which has the figure "Y_char"
Complete the first level, which has the figure "2_char"
Complete the first level, which has the figure "Long_corner"
Complete the first level, which has the figure "Plus_char"
Complete the first level, which has the figure "Triple_corner"
Complete the first level, which has the figure "C_char"
Complete the first level, which has the figure "Zigzag"
Complete the first level, which has the figure "Straight_dcorner"
Throw some figure off the platform
Complete the first level, which has the figure "Double_corner"
Complete the first level, which has the figure "Corner"
Complete the first level, which has the figure "Cube"