How do I force TDS for iOS to update achievements in Game Center?

I had an issue similar to yours, in that some of my achievements did not unlock after fulfilling the criteria. If I remember correctly, I think the buggy achievements were different from yours.

I was playing TDS on my old iPhone 4S (on iOS 7), and I think I built like 50+ floors but some achievements just refused to unlock. Then I got a new iPhone 5s, and started playing TDS from the ground up but using the same Game Center login.

In my new TDS game, I've already unlocked some of those achievements, and the rest of the unlocked achievements became unlocked on my 2nd run through the game.

So if it bugs you that you can't get all those achievements even after fulfilling the criteria, you can try resetting the game and using your same Game Center account to play the new game.

As you stated, Rebel Heroes ONLY refers to the 3 aliens you see at the bottom of your screen shot. Specifically Akbar, Chewie, and Wicket.

For whatever reason, Han, Luke, Lando, and Leia are not considered heroes by the developers. They are Men and Ladies of the Rebellion respectively.

As for why it unlocked when you purchased a different bitizen . . . My suspicion is that the achievements run a check whenever a new character is unlocked.

Game Center has always been plagued by oddities such as this, and sometimes it doesn't update if you get an achievement when you are not: signed in; on Wi-fi; or receiving cellular data.

Make certain that you are signed into Game Center, and that it confirms your log-in. Then, try to build another level. See if this fixes the problem.

It's the only way I can think of to possibly force an update.