PART 1: This is to get Just Cause 2 to launch
1. Right click Just Cause 2 in your Steam Library and select PROPERTIES.
2. Select LAUNCH OPTIONS, and type in "/dxadapter=0" without quotes. (http://i.imgur.com/YaNZ8.png)
PART 2: This is to get your graphics card to render the game (Steps 4-7: http://i.imgur.com/VAkZW.png)
1. Download Nvidia Inspector from: http://tinylink.net/nvidiainspector
2. Open Nvidia Inspector
3. Click the button to the right of DRIVER VERSION.
4. From the PROFILE menu, select JUST CAUSE 2.
5. Scroll down the window until you find: Shim Rendering Mode Options per application for Optimus.
6. Click the text to the right, scroll to the top of the dropdown, and select SHIM_RENDERING_OPTIONS_DEFAULT_RENDERING_MODE
7. Click APPLY CHANGES in the top right-hand corner.
8. Run your game
This solution has worked for me, and various other people. Hopefully this is the fix you're looking for.