[Galaxy S3 Neo Themes and Apps] TheForgotten:
With this guide, I was capable of having my phone on for 3 days with 1h of screen-on time, and 7h of screen-on time with YouTube and WiFi turned on.

I WON'T PROMISSE YOU YOU'LL HAVE THE SAME BATTERY LIFE I DID, BUT I'LL GIVE YOU THE STEPS I TOOK TO HAVE IT.
I'M NOT RESPONSIBLE FOR ANY DAMAGE THAT MAY OCCURR TO YOUR DEVICE.

With which ROM/ROMs is this tutorial compatible?

Theoretically, this tutorial is compatible with any TW 5.1.1 ROM based on MotionROM, but it was only tested in Project Lucky.

What do we need?

First, we need to have Xposed Framework installed. We also need root acess, but that comes pre-installed in the ROM.

Apps we need:

BatteryCalibration

GravityBox [LP]

Greenify (Donation Package)

PowerNap

Setting up the apps:

Greenify

First, we'll disable the auto-hibernation, because that's eats some of our precious battery. After that, we need to go to "Experimental Resources" and change the working mode to "Impulsive", then check the "Apply Greenify to system apps" and "Reveal hidden synchronization" (you can check some of the screenshots bellow).

Now, the rest is very easy, I'll give you guys a list of safe system apps to hibernate, and you simply need to hibernate those. And also, hibernate every 3rd app you install (except PowerNap), specially chat and social networks apps, those are the most battery hungry.

Calculator

Cloud Together

Camera

E-mail (both)

Studio

Galaxy Apps

Galaxy Essentials Widget

Gallery

Smart Manager

Google Play Store

Voice Recorder

Internet

Magnifying Glass/Magnifier

Music

My Files

S Planner

S Voice

Samsung Notes

Exchange Service

upday (unless you use the launcher page)

Video

Weather (unless you use the weather widget)

PS: this list was taken from Project Lucky, because it's the ROM I'm currently using.

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PowerNap

This one is very easy to configure. All we need to do is activate "Endurance Mode" and then tap on it. Now we tap on "Activation" and we drag the green ball all the way to the right, and check the "Enable while charging" box (you can check some screenshots below).

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GravityBox [LP]

Now, this one has some more steps comparing to the other ones, but it's very simple too. Go to "Display Tweaks", then "Brightness Settings". Activate it and then put the "Minimum brightness level" to 1 (check the screenshots below if you need).

Configuring the kernel:

If you didn't flash SkyKernel by [MENTION=7571048]SoUnd001[/MENTION], then do it before following the next steps. You can download it here. To configure the kernel we're gonna need an app called Kernel Adiutor. To be able to run this app, we need to have BusyBox installed. If your ROM doesn't come with BusyBox pre-installed, you can install it using an app called BusyBox. So, with the app open, we need to go to the "CPU" tab and change the "CPU Governor" from "ondemand" to "smartmax", then tap on "CPU Governor Tunables" and change the value of "enable_boost_cpu" to 0. Now, we must go to the "CPU Hotplug" tab and change the value of "CPUs Boosted" to 2 and the value of "Boost Lock Duration" to 1. Now, go to the "GPU" tab and change the "GPU Governor" to "simple_ondemand" (if you need some help check the screenshots below).

PS: in some cases, you'll lose root when you flash the kernel. To fix that, simply flash this.

Other tips for a better battery life:

Disable any kind of synchronzation

Disable WiFi, Mobile Data, GPS and etc when you're not using them

Keep Power Saving Mode always on

Keep the phone's brightness at the minimum possible

Keep auto-brightness disabled

Reboot your phone when you unplug it off the charger (connecting to the PC applies to this too)

Uninstall any app related to Facebook, like Facebook itself and Messenger