iPhone Shutdown and Battery

For the past few months now, my iPhone has been acting very strange. I'll have it on the charger all night so that its at 100% in the morning, and when I wake up, its fully charged. But here's the strange thing: every time I take it off the charger, the iPhone, after a few seconds, just reboots itself, and the battery power goes down to 10%. Afterwards, it'll reboot itself again, and the battery power will be 90%.

I've tried everything possible to fix it. I've gotten new chargers, I've tried a hard reboot (which cost me a lot of my apps and information that I stored on it), and tried not using it for the entire day to see if it will function. I'm thinking about trading it in for a new one, but before I do, I want to know if there's anything else that I might have overlooked that could possibly fix it. Any help would be appreciated.