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
Nativity Puzzle Complete!
Popcorn Puzzle Complete!
Socks Puzzle Complete!
Snowman Puzzle Complete!
Bells Puzzle Complete!
Toy Santa Puzzle Complete!
Nut Cracker Puzzle Complete!
Gift Puzzle Complete!
Teddy Puzzle Complete!
Bear Puzzle Complete!
Apples Puzzle Complete!
Mince Pies Puzzle Complete!
Cat Puzzle Complete!
Taken Puzzle Complete!
Cake Puzzle Complete!
Father Christmas Puzzle Complete!
Baubles Puzzle Complete!
Gnome Puzzle Complete!
Bridge Puzzle Complete!
Presents Puzzle Complete!
Friends Puzzle Complete!
Cookies Puzzle Complete!
Merry Christmas Puzzle Complete!
Santa Puzzle Complete!
Dawn Puzzle Complete!