Here is the full list of all 28 Package Rush achievements.
Complete Tutorial
Deliver 100 packages in one game
Deliver 500 packages in one game
Deliver 1000 packages in one game
Deliver 1000 packages
Deliver 2500 packages
Deliver 5000 packages
Play all game modes
Use all upgrades in one game
Blow up 10 warehouses
Stop time for 2 minutes
Speed up cars for 2 minutes
Build 100 routes
Build 250 routes
Build 500 routes
Make cars crash 5 times
Make cars crash 10 times
Make cars crash 25 times
Get promoted 5 times
Get promoted 10 times
Get promoted 25 times
Reach the last town in classic mode
Get 10 routes in classic mode
Collect 10 different upgrades in hand
Swap 5 upgrades with "Recycle"
Build a 100 blocks long route
Deliver package at the last second
Deliver 50 mystery orders