Other than getting parts from completing missions and side missions, you can also acquire parts by taking over an enemy's vehicle and returning it to the Catch-a-Ride system. Any time you hijack a vehicle, if you see a small numerical icon along with a car part above the vehicle's armor, this means that you will get that number of parts added to your selection by returning it. Any time you make it to a new planet, or see a vehicle driving around, hijack it and see if it is worth it.