There are several things you can do to more tightly control the timing of these notifications. I'll explain one approach and you can use this as a starting point to explore further on your own. These suggestions apply specifically to iOS apps. One caveat is that these suggestions refer to internal APIs in OFSDK 2.8 for iOS and not ordinarily recommended for high level use and subject to change in future versions.
The first thing I recommend is that you build the sample app with your own product key. Use the standard sample app to experiment before applying the result to your own code.
You are going to get the snappiest response by separating the notification pop-up UI from the process of submitting the achievement. This way you don't have to worry about getting wrapped up in the logic for deciding whether the submission is going just to the local db or is doing the full confirmation on an async network transaction.
See the declaration of "showAchievementNotice" in "OFNotification.h". Performing a search in the sample app, you will see that this is the internal API used for displaying the achievement pop-up when an achievement is earned. It does not actually submit the achievement. You can call this method directly as it is called from "OFAchievementService.mm" to directly control when the message appears. You can then use the following article to disable the pop-up from being called when the actual submission occurs:
http://support.openfeint.com/dev/notification-pop-ups-in-ios/
This gives you complete freedom to call the submission at a later time provided you keep track of the need to do so. For example, you could locally serialize a flag to take care of the actual submission either after the level is done or the next time the app starts up. Don't forget that the user could quit out of a game without cleanly finishing a level.