Very straight forward, you simply must complete the DLC level "Man of Steel" while obtaining true hero status. This can be done in about 10 minuets, simply turn on at least the 2x stud multiplier (5MZ73E) and complete the level. you shouldn't have to go too far out of your way to collect enough studs.
Maybe the most confusing part was actually selecting the level. If you are familiar with the game then you probably already know but I was not and I kept playing the story mode and waiting until I got to the game "hub" turns out any time you are in the bat cave or watchtower ouside of a level you just hit
then select "View Map" which will bring up the globe. all the DLC is at the bottom of this globe. select the "Man of Steel" level. You can unlock this in story or free play mode. Once you start turn on at least the 2x stud multiplier, the more you turn on the faster it will go obviously. Then run though the level and complete it. it will be over once you build the crib and send it off.