Diablo III
45 Achievements
1,000
60-80h
The Last of the Horadrim
Complete all quests in Act I.
25
How to unlock the The Last of the Horadrim achievement in Diablo III - Definitive Guide
* The Fallen Star
* The Legacy of Cain
* A Shattered Crown
* Reign of the Black King
* Sword of the Stranger
* The Broken Blade
* The Doom in Wortham
* Trailing the Coven
* The Imprisoned Angel
* Return to New Tristram
I think the information provided here is sufficient - this way I know that this achievement is not missable. I thought there might be (missable) sidequests that can make these act related achievemente missable, but it does not seem this way.
In order to complete all of the quests in an Act, you must go through the entirety of the main questline, which involves questgivers like Leah, Tyrael, Deckard, etc. You can skip/miss these quests if you join a friend who is a few quests ahead of you in a co-op game, however you can load up the quest that you were on once you're done playing with your friend, from the main menu of the game via "Quest Select", so the achievement is not missable.
The Act I achievements are:
The Fallen Star
The Legacy of Cain
A Shattered Crown
Reign of the Black King
Sword of the Stranger
The Broken Blade
The Doom in Wortham
Trailing the Coven
The Imprisoned Angel
Return to New Tristram