Here is the full list of all 16 wurdweb achievements.
Complete 6 Monthly Puzzles in different months
Complete 4 Weekly Puzzles in different weeks
Use undo 100 times
Complete 7 Daily Puzzles on different days
Complete 10 puzzles in Tangle Mode
Complete 10 puzzles in Precise Mode
Complete a Monthly Puzzle
Complete a Weekly Puzzle
Complete a Daily Puzzle
Complete the Tutorial
Complete 100 puzzles in Tangle Mode
Use hints 100 times
Complete 100 puzzles in Precise Mode
Place 1,000 words
Place 4,000 words
Place 10,000 words