Beating the sixth level in a chapter unlocks a boss which can appear in any of the levels in the chapter. Bosses can drop higher grade items so taking the time to kill them is a good idea. You will know there is a boss in the level if it says so on screen in the first few seconds of a level.
Mutant Boss - Throws other enemies at your vehicle and smashes you if you stay close to it for too long. This boss is fairly slow and doesn't have much health. Superior drops: Trainwreck (front), The Tool (side).
Spider Boss - Shoots webs at your vehicle. This boss likes to move around a lot and has more health than chapter one's boss so it is a lot harder to take down.
Tips for taking down bosses:
Keep moving - Bosses, like other enemies, have a hard time hitting a moving target. As long as you keep moving you will take less damage.
Use hit and run tactics - If you are not near the boss they won't do much damage to you so attack them and then retreat to line yourself up for another round.
Upgrade everything - Your car and all weapons can be upgraded to improve their stats. Upgrading weapons increases damage while upgrading your vehicle increases speed, defense or handling.
Farm previous bosses - Repeatedly killing an earlier boss in order to get better items will make killing later bosses (and completing other levels) a lot easier.