How can I earn the "...Without Bullets!" achievement?

Your grappling hook can be used to pull down/apart any chaos objects, or sling explosive barrels into them. Alternatively, you can drive vehicles into things.

The grappling hook is the easiest method and the easiest base to achieve this is Cima Leon: Silo. There are only a few chaos objects in the base and they are all easy enough to break with your hook.

The base is on the first island and the co-ordinates are N 40 41.334 E 5 43.546