Stuck again here. I"m kind of wondering around now, and don't seem to be accomplishing anything for a while.
I finally made it through the Renegades, where I had to swing and make it under the lowering gate, then on through the headquarters, where i jumped the boulders, got the gas mask, and then came back out the way I went in.
Next I passed back through the Renegade village, back through the Butterly place where I was able to go get the idol with my gas mask this time. I went back through Turtle Village, got the idol in the cave there with the native's help. Now I've finally ended up back at the Flooded Courtyard, because that is where the map seemed to be guiding me. However, I don't see what else to do here. The one thing I hadn't done before, which I did this time, was to swing on the vines off the left side of the temple. But it seems that you have to had blown up the barrier before you can land off that vine without falling back into the water.