Alexim: Maybe also Deadmarye can help us.
Sure ! So I started a game in the demo and selected the middle option for the three column (+1 Final Score each).
I can confirm what musturiuz said : The game stops after building The Sanctuary of the Falcon which was done at turn 37 for me (again, I'm not great at 4x).
To the contrary of the full game where reaching the final turn limit (Turn 220) lets you continue in Free Play, in the demo reaching that point means it's over. You can either start a new game or quit it, meaning that any achievements you could gain after The Sanctuary of the Falcon cannot be obtained in the demo.
What I got during my normal playthrough are the following :
-Scout (Scout Any Region)
-New Knowledge (Discover any technology)
-Permanent Settlement (Build the Field of Grain)
-Bronze Falcon (Get the Bronze Victory in the Sanctuary of the Falcon Trial.)
-Silver Falcon (Get the Silver Victory in the Sanctuary of the Falcon Trial.)
Regarding the Falcon achievements : it might be possible to get Gold Falcon and Divine Falcon (Complete the Sanctuary of the Falcon trial without spending food or production) too.
Now, I believe any other achievements to be locked out of the demo :
-Every achievements tied to a trial are obviously unobtainable.
-Achievements regarding doing X things (Create x Workers, Achieve X ressource per turn, build x thing in x region)
-As well as those about exploration (Trader, International Trade, Good Soul, Diplomat, etc) since you do not have access to the map of Egypt.
-The ones related to Turns (4000 BC, 3600 BC, 3300 BC, 3060 BC)
-Of course, any achievements related to winning the game (Winner, The Master of Fate, Wise as a Warrior, etc)
In a very long grind, it might be possible to get "Follower of Horus" (Honor any incarnation of Horus 100 times during all games) but that's not recommended in the demo.
One might also look into "Friend of the Gods" (Achieve+10 or more authority growth per turn.) I'm not sure it's possible in the time available but I could be wrong.
Any more informations will be gladly taken ;)