Here are a few considerations when taking pics of chams:
1 - lenses have a minimum focusing distance. I have a camera that uses detachable lenses (I know yours is a point and shoot but...) for close up work I need a close up (AKA macro or micro) lens that allows me to get very close to my subject. For example, I have a 200mm micro lens that will focus down to 10 inches from my subject, compare that to my normal 200mm regular lens that has a minimum focusing distance of just over 6 feet. Though you have a point and shoot, your built-in lens will have a minimum focusing distance as well. Stand too close, your pics will be blurry.
2 - shutter speed. You have to use a shutter speed that is not only fast enough to stop the movement of your subject but also yours. Everyone's hands shake and the bigger the focal length, the more noticeable it becomes. Rule of thumb is that if hand holding you should use a shutter speed equal to or greater than the focal length of your lens. Thus, I'd want a 1/200 second or faster shutter speed if hand holding my 200mm lens. Thats going to require a lot of light. If you zoom in on your chams (disable digital zoom BTW) you'll really have to hold that camera steady to get a clear pic. Make sure your anti-shake is turned on and/or use your flash. If you are using very slow shutter speeds - 1/20th or so - you will get blurry pics even when using a tripod (if anti shake is turned off) because the camera will move as you press the shutter. Your camera records all the settings used so I'd recommend looking at the data and see if you can learn something from it.
3 - back-focus. This is when the camera focuses on the background rather than the intended subject. You'll see this all the time in pics posted on this forum - look for it - it'll make you a more critical photographer. Realize that your camera doesn't know what you are taking a picutre of and will focus on most anything that is of decent size in the middle of the frame, like the screen on the back of your cage or a large leaf. Many times your camera won't be able to find the small chameleon. This is a very common problem so be very critical before hitting the shutter.
Hope this helps