The general strategy for Ham ’em High level 12-4 is to loft a Yellow bird and accelerate through the middle structure. With a little luck (see method #2), you can detonate the central TNT and clear the level with a single bird. Otherwise, fire a Yellow bird into the top of the first stone tower and detonate the TNT beyond. The score in the video below is 81,260.
Method #2 yields 87,950 using one bird, which is just about the same as the method above. It took me about 10 tries to do this level similar to the walkthroughs. The big stone triangle in the middle kept getting stuck between the two long support boards, so be sure to take the one on the left out first.