That doesn't work that way this month it seems. It has to be a total of 12 different puzzles. No matter how many times you do same the puzzle it only counts once, even if you do it with different characters.
Considering the achievement is "only" a total of 12 puzzles it makes sense that at least they require you to complete 12 different ones.
Also consider that this month for the first time in a monthly you can get to choose 4 out of a bunch, so if puzzles are not your forte you can try another thing.