The solution above provides a good guide on how to go about getting the alien icons for each level. There is, however, one icon that is especially elusive. It's located on the meteor crash site level. As you begin the level turn left and look for a small white skeleton on the ground. Drive over this to free the icon. I spent ages looking for this damn thing. I cleared the level of all other destructible objects twice before I looked up its location online. Judging by the posts in the topic I found it seems a lot of people have had trouble with this icon. So if this one is bothering you then I hope this helps.
Credit should be given to YanniOblivion on Gamespot for asking the developers for help which resulted in its location being uncovered.
Other than that you just have to destroy everything on each level. Literally, everything. Rocks, small trees, fence posts, road sign posts, those junctions that connect sections of pipeline in the oil fields, everything that can be damaged may yield an icon.
NOTE - The small bushes that you can drive over in the meteor level do not hold any icons. The small trees do but the smaller brown bushes do not.
If you need any further clarification on anything then feel free the message me on here and i'll get back to you ASAP.