I suggest to check for physical problems with the battery first. Does it appear to be swollen or bloated? Does it spin easily when it is lying on a flat surface? If so, the battery has failed and continued use can be dangerous. See this topic for some (extreme) examples.
If in the battery overview (under settings) you see strange sudden dips, this could also point towards a failing battery.
In some cases a defective SIM card can also cause a high battery drain - if the drain is significantly lower when there is no SIM card in the phone, that could also be the case (though this is somewhat rare).