Update: The steps below worked. I earned a lot of achievements that I couldn't before. Tried the merbaby with two different families and it still isn't working though

Some achievements are not showing up in the list of achievements in my game. Such as the Plenty of Fish one where you are supposed to have a mermaid baby. I had the a merbaby and it did not unlock. Later on the same playthrough/save/same everything I unlocked the achievement where you make drinks at the barista bar. The barista bar achievement had been listed in the incomplete badge list, unlike the merbaby one.

The only possible solution I found is this. It is from another sims forum:
"How to change it then?
I found out that the problem was that the file didn't get updated. This is was I did to fix it:
1. Rename your "The Sims 3" folder, so that when you start the game a new folder will automatically be regenerated, meanwhile keeping your data in the renamed folder.
2. Start the game
3. Start up any new game, choose a family and play for a few seconds or so.
4. Now you should get a message in the top right corner of your screen like "there are new Achievements (or Badges) available".
5. Check your achievement badges in your profile in game. For me, now I finally had a total of 265 possible badges, instead of only 112.
6. Don't think you have to save the game after this, because the file is updated and seems not related with a save, but I saved the game just to be sure.
7. close the game
8. Make an extra copy of your original The Sims 3 folder, just to be sure you don't loose anything.
8. from the current (newest)The Sims 3 folder, copy the file The Sims3\Downloads\74998114.........\ChallengeData.package to your original The Sims 3 folder and replace the old ChallengeData.package file. (Make sure you're in the correct folder!)
For me, the new ChallengeData.package file was over twice as big as the original one, which makes sense since I had a total of 112 before and now 265.
9. This is it. You can change the name of your newest The Sims 3 folder to for example "The Sims 3 test" or you can delete it.
10. Change back the name of your original The Sims 3 folder
11. Play and enjoy."

What about cases where the badge description does appear in your game, but they never complete after you have met the requirements to earn them?