UPDATE (24 September 2015) This is fixed!
Saints Row's Discontinued Achievements Now Fixed---
First off, you must have a current Xbox LIVE Gold Membership and a Saints Row Community account in order to upload or download characters. Either create this account on the console or via saintsrow.com. Log into the account via the Community section on the main menu or confirm your login during the following process.
Either during initial character creation or while in Image as Designed, scroll down to 'Character Gallery'. Choose 'Upload Character', confirm your choice... and be rewarded with 10G.
Note that any characters uploaded will need to be processed through your saintsrow.com account to be downloaded at a later date.