First, you need at least 4 hability points in Long Distance to unlock deliveries up to 1,100 km.
After that, just pick a delivery that has more than 1,000 km and be very cautious during that job. You can do it with your own truck or with a quick job.
Tip 1: Don't use the cruise control during this delivery. It helps to you manually control your velocity, so more easily avoiding fines.
Tip 2: Be extra sure when crossing preferential roads. Sometimes the game's IA have some misbehavior.
Tip 3: Save a lot. You can always load a saved game if something went wrong.
Tip 4: You actually can damage the truck, but not the trailer. I finished my job with 2% of truck damage and 0% of trailer damage and still got the achievement. Although I was very cautious and never hit the truck on anything during the travel, I think this 2% of damage are the natural tires/engine/transmission/chassis/cabin wear.