Careerist
Uncommon34.8%ObjectiveOptionalAnywhere
Complete 5 jobs in a row - in-time, without taking any damage to cargo and without using autoparking
Do as the achievement description describes. A little truck damage is ok and won't invalidate progress. Traffic penalties don't invalidate it either. For parking, the simple parking (the middle option) is fine - only skipping parking altogether would invalidate the achievement progress.
So long as you drive reasonably carefully and avoid skipping parking altogether then this will be easy enough to unlock just a few missions in.