First board: You need to focus on the mud block at the top of the center column. It's really important that you destroy it as quickly as you can. So, what you basically need to do fast, is to destroy that mud block, using rockets either from left or right side. This is your main goal. If you have nothing else to do, you can hit those broken stones, but it's not what you should focus on. After you've destroyed the mud block, diamonds will fall into the center column. Match all the combos you have available there. When you run out of possible combos there, use the rockets from either side to help you destroy the remaining ground blocks/broken stones. You should proceed to the next board with at least 4-5 moves. The more the better, but with 4-5 moves left you should be able to reach the minimum required score.
Second board: It's a Treasure Room. Match combos with most number of "big" diamonds. Use Color Burst from Magic Orb immediately, so that you allow more "big" diamonds to appear.