Credit to HappyThumbsGaming for the descriptive guide:
Darkseid is automatically unlocked when you download the Bizarro Pack, once in the HUB travel to the moon. Once on the moon switch to Darkseid and the achievement will unlock. It seems that the achievement will not unlock if you travel to the moon with Darkseid in your party, simply switch to a different character and then switch back for the achievement to unlock.