battery drain

I have had my iPhone 5c for over a year now. I updated it to IOS 8.1.2 and noticed a dramatic battery drain, this was going on for a while so I tried all the battery saving tips, closing apps down, turning auto brightness off, pretty much everything you could do to save battery and nothing was working, when I charged my phone it would sometimes get hot. My battery life could last about 8 hours, i could have it charged at 100% leave it overnight and the battery would be at 10-20% whereas before the update I could easily go a day without charging my phone, I only have a few apps, mostly social media, spotifty. When the 8.1.3 update came I thought this would help, no luck unfortunately. I changed my battery and that didn't help either, I heard you should re calibrate and i'm in the process of doing this but has anyone had any problems similar to this and any solutions??

Thanks.