Chapters, Parts and Paints are unlocked in the game by beating bosses. The following is a list of what is available and which boss has to be beaten to get it.

Chapters

Unlock Chapter 2:
Beat Taz.

Unlock Chapter 3:
Beat Ender.

Unlock Chapter 4:
Beat Nick F.

Unlock Chapter 5:
Beat Big Lou.

Unlock Chapter 6:
Beat Zoe.

Unlock Chapter 7:
Beat Sol.

Unlock Chapter 8:
Beat Izzy.

Unlock Chapter 9:
Beat BBB.

Unlock Chapter 10:
Beat Earl.

Unlock Chapter 11:
Beat Sassy.

Unlock Chapter 12:
Beat Webster.

Unlock Chapter 13:
Beat Orca.

Unlock Chapter 14:
Beat Terry.

Unlock Chapter 15:
Beat Murff.


Parts

Unlock Rims 1 - 5:
Beat Ender.

Unlock Rim 6:
Beat Izzy.

Unlock Rim 7:
Beat Izzy.

Unlock Rim 8:
Beat Izzy.

Unlock Rim 9:
Beat Izzy.

Unlock Legendary Brakes - Carrera GT:
Beat Razor.

Unlock Legendary Chassis - Golf:
Beat BBB.

Unlock Legendary Chassis - IS300:
Beat BBB.

Unlock Legendary Chassis - M3 GTR:
Beat Razor.

Unlock Legendary Chassis - TT:
Beat Orca.

Unlock Legendary Engine - RX-8:
Beat Orca.

Unlock Legendary Turbo - Mustang GT:
Beat Orca.

Unlock Spec 1 - Body Kits:
Beat Big Lou.

Unlock Spec 1 - Brakes:
Beat Nick F.

Unlock Spec 1 - Chassis:
Beat Taz.

Unlock Spec 1 - Engine:
Beat Zoe.

Unlock Spec 1 - Turbo:
Beat Big Lou.

Unlock Spec 2 - Body Kits:
Beat BBB.

Unlock Spec 2 - Brakes:
Beat BBB.

Unlock Spec 2 - Chassis:
Beat Sol.

Unlock Spec 2 - Engine:
Beat Sassy.

Unlock Spec 2 - Transmission:
Beat Ender.

Unlock Spec 2 - Transmission:
Beat Izzy.

Unlock Spec 2 - Turbo:
Beat Earl.

Unlock Spec 3 - Body Kits:
Beat Orca.

Unlock Spec 3 - Brakes:
Beat Webster.

Unlock Spec 3 - Chassis:
Beat Webster.

Unlock Spec 3 - Engine:
Beat Murff.

Unlock Spec 3 - Transmission:
Beat Orca.

Unlock Spec 3 - Turbo:
Beat Terry.


Paint

Unlock Boss Paint - BBB:
Beat BBB.

Unlock Boss Paint - Big Lou:
Beat Big Lou.

Unlock Boss Paint - Earl:
Beat Earl.

Unlock Boss Paint - Ender:
Beat Ender.

Unlock Boss Paint - Izzy:
Beat Izzy.

Unlock Boss Paint - Murff:
Beat Murff.

Unlock Boss Paint - Nick F.:
Beat Nick F.

Unlock Boss Paint - Orca:
Beat Orca.

Unlock Boss Paint - Razor:
Beat Razor.

Unlock Boss Paint - Sassy:
Beat Sassy.

Unlock Boss Paint - Sol:
Beat Sol.

Unlock Boss Paint - Taz:
Beat Taz.

Unlock Boss Paint - Terry:
Beat Terry.

Unlock Boss Paint - Webster:
Beat Webster.

Unlock Boss Paint - Zoe:
Beat Zoe.

Unlock the cars which you can buy from the Safehouse by beating certain racers from the Blacklist.

Porsche Carrera GT:
Beat Orca

Ford GT:
Beat Orca

Mazda RX-8:
Beat Big Lou

Ford Mustang GT:
Beat Big Lou

Subaru Impreza WRX STi:
Beat Big Lou

Audi TT 3.2 Quattro:
Beat Big Lou

Corvette C6:
Beat BBB

Lotus Elise:
Beat BBB

Lamborghini Gallardo:
Beat BBB

Lancer EVOLUTION VIII:
Beat BBB

BMW M3 GTR:
Beat Razor