MacBook Pro goes into hibernation immediately after login, how do I fix this? My Mid 2012 MacBook Pro, goes into hibernation immediately after logging in. Battery indicator still shows around 95% charges when it does that. When I plug in and reboot, battery shows 0%.

This does not happen if I just let it stay in the login screen for, say 2 to 3 hours. The battery can stay for about that long which is I can say is the normal for it. At least before this issue arises.

Might this be just calibration issue? Is it fixable without having to be brought to service center?
If you've reset the SMC and it's still showing the problem, then you will need to take it in to an Apple Service Centre. The 13-inch 2012 MBP is still supported, as it was sold up to October 2016. 

The 15-inch model is considered "Vintage" and Apple no longer provides hardware support. (Though it might be worthwhile taking it in anyway and smiling sweetly: my local Apple Store says they will continue to fix vintage hardware if they still have the parts.)

Batteries are the one part of a laptop that you can expect to fail over time and need replacing. If you can get it replaced, then that's a small price to 'refresh' your laptop and extend its useful life.