NOTE: The bonus level is available once you have completed the main story.
The bonus level is located in Erebor. It appears as a Stone Giant icon just south of the second ‘R’ in ‘Erebor’. Fast travel to the Erebor “The Lonely Mountain (South Region)” statue. Open your map and mark the Stone Giant icon as your destination. Travel southwest up a stone wall where you will reach a ladder hidden by snowmen. Break them and climb up. Now you can one of two things, use an elf to reach the top of the tower or use Bilbo (to build a wraith ladder) and Ori (slingshot targets to build platforms) to find a path up. Regardless of which option you choose, once at the top, move across the tight rope and the entrance to the level is on the ledge.
The goal of the bonus level is to collect 1,000,000 studs before the five minute timer expires. You are playing as a Stone Giant, so just stomp and smash everything possible; there’s more than enough studs available. You should complete this in roughly three minutes.
It is also possible to unlock the “Someone to share in an adventure” co-op achievement. Since this level is very short, plug up another controller before starting the level and just let it idle as you collect your studs. You will receive both achievements when you are done.