To earn this trophy, you must purchase all 8 of Moxxi's Moxxtails in her bar.
Each Moxxtail requires 10 Moonstones.
The simplest way to earn this is gather 80 moonstones, go to Moxxi's bar and save, then purchase each Moxxtail.
Once the trophy pops, go to the dashboard and close the game down without saving. When you go back into the game you will be in the bar with all your moonstones having not spent them.
You
do not need to wait for each Moxxtail to time out before purchasing the next one.