Solution 1:

unfortunately this wont be possible, unless it's available on the SD card.

If it is, you could try

  • http://www.ehow.com/how_7878352_recover-erased-nintendo-ds-file.html

be sure to try the following steps as well

  • http://en-americas-support.nintendo.com/app/answers/detail/a_id/51/~/how-to-restore-save-data
  • http://en-americas-support.nintendo.com/app/answers/detail/a_id/542/~/pre-installed-software-is-missing-or-deleted-%28nintendo-3ds%29

If that fails (because it no longer is in the store) you'll need to contact Nintendo directly. Don't worry, they have a great customer support!

be wary, games are linked to a nintendo network ID in some cases.. so that might be a part of your problem as well!