The achievements have nothing to do with game saves dave.
BoSox, if you never deleted any game saves from your harddrive, or ever replaced your harddrive or xbox since you had oblivion, chances are that the save file(s) are still stored there. If they are there, yes, owning the game you will be able to use your
save files. If you want to check to see if they are actually there follow these steps.
Go to settings on the top far right of the dashboard.
Choose the System Tile.
Choose Hard Drive (or Memory Unit)
Choose Games and Apps
Look for Oblivion, if you see it Select Oblivion.
Look for Save files (do not delete anything)
If you find save files there, then you still have them.
Have fun with Oblivion, great game!
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