Chosen Solution
Just replaced iphone 6s battery with ifixit iphone 6s battery replacement kit and guide. I followed the instructions including draining battery and charging it fully. The iphone shuts down at about 80%. It will not turn on until it is plugged back in to a power outlet with the apple charging cable.
its possible that the battery just needs to be calibrated but after a few charging cycles and the problem is still there i would consider contacting Ifixit and letting them know and they might send a replacement battery.
If recalibrating the battery does not work, try restoring the iphone as new. If you are still having problems with the phone after restore, I would try contacting iFixit and see if they will give you a replacement battery.
I have erased all contents and setting on the iPhone and restored back to factory settings. The iPhone was still shutting off and I needed to plug it back in to start it again. I checked the battery with Coconut Battery and it still read that it is functioning well and fully charged. I then tried to see if the phone would power off if I kept the screen on and started the stopwatch. It stayed on. I then realized I needed to turn off auto-lock. Settings>Display & Brightness>Auto-Lock>Never. So far this seems to work. I was so frustrated and almost opted to just buy a new iPhone, hopefully this resolves the problem for good.