I don't know your camera, but I did a quick google... your camera has spot metering mode, you can try that to help on some of the backlit scenes. That would help expose the subject properly, but for sure would overexpose the bright areas even more.
Or try your 'Backlighting' scene mode. After selecting that scene mode you can then choose to turn HDR On or OFF. Try both. OFF fires the flash to help with the shadows. That could work well on very close subjects. ON takes two pictures (maybe more than 2, I can't tell from my quick read) and combines them. That might be tricky without a tripod.
You might be happy adjusting lights and darks in post processing like eyelight said.
Also take a look at focus modes and try single point focus. This can help for a bird in the tree or animal in the brush or any scene where YOU want to be sure of what is in focus. Otherwise, focus may fall on the nearest tree branch.