One strategy for Ham ‘em High level 12-12 is to launch the first Blue bird through the first small structure. Fire the next two Blue birds through the middle ice tower. The score in the video below is 80,040.
Method #2 yields 83,810 points using only 2 birds. Fire the two Blue birds into the left side of the main ice tower. With a little luck, the falling tower will take out the pigs on either extreme of the central tower.