To unlock Overtime mode and complete The Facts, you have to complete every story-related mission (the yellow diamond) to its fullest. The only real turning point comes during Chapter 7. For this quest, you have to retrieve Annie from the karaoke bar. But, Gary is blocking the way. At this point you have two options:
- Kill him.
- Retrieve Rhonda, his ex.
To complete the Facts and continue into Overtime mode, you have to chose the latter and reunite Gary with his ex.
Since this is the only prerequisite, you can just reload Chapter 7 after finishing the game if you for some reason miss it.