Package missions are given by the NPCs standing around Glass and are split into Fragile and Covert deliveries - the latter being runs where you dash from A to B and avoid K-Sec cameras or groups, and the former being runs where you're entrusted with a keepsake of some sort by the NPC to deliver to someone close to them (emotionally, that is - distance-wise they're a little further away).
It's the latter mission type you'll want to go for to get this achievement. You'll want to deliver the package with no cracks - signified at the top of the screen - the game is lenient and lets you get two cracks for free, and the third will fail the mission. However, for the achievement, we want no cracks.
Cracks happen when you take a heavy landing, so use the skill roll when falling large distances to mitigate the impact and you'll get this pretty easily on some of the earlier delivery side activities. I used the mission in this video: