I had the same problems with this model of laptop and I found that if you install "Linux Mint 13 KDE Maya 64 bit" (get *.iso from their website) and RADEON video driver amd-driver-installer-12-6-x86.x86_64.run (search for it on AMD website) everything will be OK!! You will have ~4h of battery and fan will even stop sometimes, and you can change between the dedicated RADEON card and Intel card using the amd ccle and then log out/log in.
I would post an image with a screenshot of my desktop to show you that this setup works, but I don't have 10 reputation points ...
Newer drivers from AMD don't work with latest Ubuntu 12.10 because Ubuntu has the latest version of Xorg/Xserver which is not supported yet by AMD drivers (read the release notes). So, in order to have a working setup you need a Linux distribution which has a compatible version of X.Org with the driver you need to install. Linux mint 13 has X.Org 7.6 which is compatible with RADEON driver 12.6 which "knows" 7.6 (read the release notes).
1) Never install updates in Linux Mint after you installed the AMD driver 12.6.
One day I installed updates and laptop got stuck at a black screen during boot.
2) To enable/disable "3D effects" in KDE press "Alt + Shift F12" this will improve FPS in games and maximize battery life. Minecraft works fine on Linux Mint (around 60 fps? if I remember well).
3) If somebody needs help on how to install AMD drivers, they can find working instructions HERE which I wrote.
4) Linux Mint Maya is LTS and has support until 2017, plus it is fully compatible with all Ubuntu applications.