Looks a common issue with Samsung, similar with an SG S3

Battery showed 100%, but only last 2-3 hours, drain quickly. Hard to charge up. When reach 100%, drop to 50% or so in 10min, then drain to 10% in 2-3 hours even doing nothing (wifi off, apps off, only 3G on). No luck with factory reset. Not battery issue either.

The problem was finally resolved by sending in to Samsung for a repair (not sure what they did).

Common issue if you do a web search. Possibly a combinaiton of hardware and software issue. But Samsung never admiitted there's one.