Two things to fix,
one, adjust your brightness to auto. The higher the brightness, the faster your battery dies, that is massive screen use.
two, poor wifi/cellular reception = ****ty battery, the phone uses more power to lock onto signal.
Dont use task killers, they do more harm than good.
I adjusted the brightness on my tbolt and I doubled battery life
Moto V188 -> RAZR -> BB 8100 -> BB 8900 -> Thunderbolt -> DROID RAZR HD -> Galaxy Note 3
If I helped you, hit thanks!