1. Start up any service with passenger loading with a last step of LOAD PASSENGERS and play through it as normal.
2. When you are on that last step, just before the load passengers ring finishes filling, pause and make a save.
3. Complete the service and return to the main menu after.
4. Load up Last Played and complete the service again.
5. Repeat until the achievement pops, making sure you exit to the main menu and load Last Played after each service completion.
The tracker doesn't work for this achievement so you'll have to keep track on your own how many you have done.
Doing it this way should also unlock the following achievement, assuming you're starting both from 0. If not you may have to adjust how many you need do to finish the other achievement as well.