So I tried gathering 1000 grass and kept a thorough record, but even at 1100 (by my count) the Achievement didn't pop. Keep in mind I did do a New Game+ somewhere in the middle of my grass gathering, so either grass gathering Achievement is still expecting you to gather 5000 grass or the New Game+ might have nulled my gathered grass statistic...

* Note: If you're basing any Achievements on player game statistics (like, islands visited, distance sailed on a boat,stone/grass gathered etc.) - you should have stats screen that displays these values and players can check themselves the progress...