Act 1 is made up of the following missions in order:
Fellowship
The Eyes of Sauron
Shadows of the Past
Ruth
The Seeing Stone
Knife in the Dark
No Man's Land
Rain of Arrows
Traitor's Gate
The Arena
Before Dawn
The Fall.
Concluding with the Fall.
*** Spoiler - click to reveal ***The Fall has about 4 parts to completion. However the achievement popped for me after part 3 and its following cutscenes. Playing on easy, so the requirements could be different on the harder difficulties. Unsure.
1st part you defend a section for bout 2 minutes.
2nd part you fight these shadow knights.
3rd part you have to get to the spider Shelob and assist her. Once you finish this part here, the map opens up and the cheevo should pop round here.
4th part. You gain the domination ability. You start by dominating 10 archers. Followed by killing/ dominating 25 enemies.
Thanks for your time and hopefully this gives you an idea as to when the first Act ends.