Here is the full list of all 27 Pixel Puzzles 2: Christmas achievements. It takes around 4-5 hours to unlock all of the achievements on Windows.
Complete Santa Hat
Complete All Puzzles
Cake Puzzle Complete!
Cookies Puzzle Complete!
Apples Puzzle Complete!
Presents Puzzle Complete!
Bear Puzzle Complete!
Father Christmas Puzzle Complete!
Popcorn Puzzle Complete!
Nativity Puzzle Complete!
Cat Puzzle Complete!
Santa Puzzle Complete!
Merry Christmas Puzzle Complete!
Socks Puzzle Complete!
Friends Puzzle Complete!
Gift Puzzle Complete!
Snowman Puzzle Complete!
Teddy Puzzle Complete!
Taken Puzzle Complete!
Nut Cracker Puzzle Complete!
Gnome Puzzle Complete!
Bells Puzzle Complete!
Toy Santa Puzzle Complete!
Dawn Puzzle Complete!
Mince Pies Puzzle Complete!
Baubles Puzzle Complete!
Bridge Puzzle Complete!