Building off what Skeptical Mario has said, here are a few tips that helped get me over the hump in finishing stages 4-6.
MAKE AS MANY CONSECUTIVE CHAINS AS POSSIBLE! Don't forget you can switch the ball you shoot with whatever one is next in line by hitting either the LB, RB, or the B button. You can see which color is next through the hole in the stone frog's back. Once you "ZUMA" the level, you don't need to worry too much about keeping the consecutive chain going. Just clear what's left as quickly as possible to get max points.
COINS - Though be careful if you try to shoot a coin while making your chains. An errant shot will start over your streak of consecutive chains if you miss completely and/or hit the line of balls. Shooting the coin will not mess up your consecutive chain streak.
Most of all, just relax, concentrate, and make your shots. Hope this also helps you guys out in netting this achievement. Good luck!