The sixth Chrome Dimension level can be unlocked from a chrome ‘egg’ found in Level 3-7. Here is a video demonstrating how to get the egg. You should take a look at the Chrome Control guide for information on controlling this.
For your first hit, you want to take out the pig on the left. From there, use the second hit to weaken the structure. For your third hit, take out the right portion. For your last hit, take out the rest of the structure.