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