There's two locations where you can create a Custom Character: The Watchtower's Lab and the The Batcave's Lab.
In these two locations, there's a character customizer, simply pick random, save and you'll unlock the achievement.
However, there are some missions where you need to create a custom character with certain outfits, such as the Booster Gold mission, the Penguin mission, the Supergirl mission, etc. This is probably where you will unlock it for the first time.
Here's a guide in case you're having trouble with finding the customizers: