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