1. If you want to get your Minecraft-Achievements and -Stats back, please read and follow all of these 10 steps.
2. First of all; Back up all edited files (they are: stats_[Username]_unsent.dat from your old AND new Minecraft (if exist)), or better yet, all Minecraft files.
3. Open your stats_[Username]_unsent.dat file from your old Minecraft-Version with a text-editor. You can find this file located at .minecraft/stats.
4. Copy-paste the whole content from the file into the input field on this website.
5. Click the button "Generate new Code" (this may take a while).
6. Copy your stats_[Username]_unsent.dat from the old Mincraft-Version into the new one, replace existing file (you made a backup of it, did you?).
7. Open the new (old), copied file and put the code you get here into "checksum":"[LotsOfNumbersAndSomeLetters]", replaceing the old "[LotsOfNumbersAndSomeLetters]" with the new one.
8. Make sure, that you copied ALL symbols, didn't get a double "", didn't replaced the "checksum" or the : and there still exist the last }!
9. Be aware that there may be a part has been lost (those stats are marked RED in the list, you need to delete this lines from the new stats_[Username]_unsent.dat file, otherwise Minecraft wipe the complete file again).
10. Try it and keep your fingers crossed...