To get this achievement, you only need to beat each level on each island. You do not need to get the gold masks. I've taken pictures of all of my winning level configurations, but that may not directly equate to beating the levels for you. I found that the way things fall, the monkey's effect on the sticks, and the final outcome of the level are non-deterministic. I would occasionally beat a level without changing anything - just restarting the action seemed to make it work. So, take the pictures as a starting point,a nd adjust them as needed to get to the winning combo.
For the pictures, they were taken after I beat the Eco challenge for each level, so they use fewer bamboo sticks than are needed Also, some levels needed two pictures, so you will see some a/b pictures. a is generally the top of the level, and b is the bottom.
http://tikitowers.4shared.com/Also in that link is a complete list of islands, levels, and eco targets for left over bamboo.