Here is the full list of all 21 A Familiar World achievements.
Finish one puzzle on the difficulty easy
Finish five puzzles on the difficulty easy
Finish ten puzzles on the difficulty easy
Finish 15 puzzles on the difficulty easy
Finish 20 puzzles on the difficulty easy
Finish one puzzle on the difficulty medium
Finish five puzzles on the difficulty medium
Finish ten puzzles on the difficulty medium
Finish 15 puzzles on the difficulty medium
Finish 20 puzzles on the difficulty medium
Finish one puzzle on the difficulty hard
Finish five puzzles on the difficulty hard
Finish ten puzzles on the difficulty hard
Finish 15 puzzles on the difficulty hard
Finish 20 puzzles on the difficulty hard
Finish one puzzle on the difficulty advanced
Finish five puzzles on the difficulty advanced
Finish ten puzzles on the difficulty advanced
Finish 15 puzzles on the difficulty advanced
Finish 20 puzzles on the difficulty advanced
Finish one puzzle on the difficulty expert