A destroy the object level is one in which you have to destroy different types of objects to complete the level. Just use your rockets to demolish all the objects without hitting an enemy. Enemy friendly fire that results in other enemies dying is okay. This is ridiculously easy to do on Level 3 of the main campaign. NOTE: Level 3 has a few specific enemies that you will miss if you complete it without killing any enemies, which are required for the "The Things I've Seen" achievement. Make sure to replay it an kill some of the enemy types to unlock them.