This is a fairly easy and straightforward trophy to get, especially if you have already initiated the Thieves Guild questline.
NOTE: The Thieves Guild questline
does not need to be initiated to change your face and earn this trophy.
Inside the Ragged Flagon, which is accessed through the sewers in Riften, is a woman named Galathil. She is sitting on a bench by herself and is wearing white robes with a red hood.
Simply speak with her, pay her 1000 gold, and enter the character creation screen.
You do not need to make changes to your character. If you like the way your character is, simply back out of the creation menu and you will still earn the trophy.
Alternatively, to keep you 1000 gold, save the game, pay the gold, earn the trophy, and reload the save file from before you paid her.