To unlock the Pandora-dog Millionaire trophy in Borderlands: Game of the Year Edition, you will need to have collected a total of $1,000,000. The total is accumulative, so you don't need to have the full amount in your possession at once.
You can track your progress towards the trophy by going to Menu > Quest Tab > Press
to view challenges. The challenge you want is called
The Rich Get Richer.
This will most likely come through natural play if you are looting everything you come across in the world, and selling items you don't need.