Achievement obtained offline, does not appear online after update Dashboard.

Some of your achievements obtained offline can only be obtained online, which means you cheated .

Case Closed.

You lost the achievements because you obtained them on an offline profile, and then recovered your profile from the online database. In other words, because the offline gamercard never connected to XBL, the online database
wasn't updated, so you downloaded an older version. Hope you get that, find it hard to explain over text sometimes lol.

Regarding obtaining those lost achievements, have you tried clearing your cache on your xbox and tried to obtain them again? May be worth a shot.

Hello,

Those achievements are not obtainable any longer. You can simply play the game offline and earn all of the offline achievements. You wouldn't be able to 100% the game if it has achievements that require online when their servers are offline.

To resolve, set the connection offline. As soon as the dashboard appears, select settings and set the console online again. The update will start automatically.

There's no way to help them obtain those achievements. When a game's servers are going offline it's up to the publisher to communicate this to customers and let them know (EA does this). They have a cut off date, after that period you can't get online anymore,
that means that you can't get those achievements anymore. Microsoft has nothing to do with helping people unlock achievements from a 3rd party game.