This video shows you one way to achieve 100% Total Destruction on Angry Birds Surf and Turf level 12. If you have an alternate strategy please feel free to leave a detailed comment below.
Fire the Yellow bird into the left side of the jigsaw structure. At the least, you want to clear the pigs in the right trench. If you clear all pigs, act quickly. Use two White Birds to bomb the trees on the left slope. Land the Sardine Can on the lowest branch on the left side, or alternatively loft it into the right trench.