I have just started a level, quickly got an achievement I needed. Now can I just quit the level and still have the achievement or do I have to play and complete the level before I gain the achievement?
No you don't have to complete the mission, however you do have to be connected online.
No, you just need to meet all requirements for a certain achievement to obtain it.
- You must be online
- You must not have cheated during the mission or any other mission before on this particular scenario / save game.