This is story related and can not be missed. See the spoiler below for about when it should unlock.
*** Spoiler - click to reveal ***
After saving the town from the walkers a 3 day time jump will occur. After this jump and some dialog, you will walk outside and talk to Jesus. Durring this conversation, he will ask you to step up and lead the town. After making a decision and loading screen the achievement should unlock
Sometimes achievements in the game do not unlock when they should. I recommend creating a copy of your save after completing chapter 4 ep 5 in case this happens. Otherwise you may have to replay the chapter from the beginning.
You can create a copy of your save from the main menu by:
1. Click Settings >> Saves
2. Press
on your save.
3. Select a different save slot to create a copy there