You will most likely get this without even trying. If you are a serial-hoarder, like myself, you will find yourself selling a lot of stuff to acquire different stuff.
If you are looking for a fairly quick way to get the trophy then you should stock up on items that have great value. Weapons like Laser and Plasma rifles will catch a great price. Anyways, stock up on lots of stuff and head to the Gun Runners vendor who is in a kiosk outside of Freeside.
Important! SAVE your game before you talk to him!
Sell EVERYTHING in your inventory to the vendor. He only has 8000 caps to offer you but make sure you take it all. Then go and fast travel to either Chet in Goodsprings or another vendor of your choice and get the remaining caps you need.
After you get the trophy, reload the hard save you made right before you sold everything. Then you can just sell stuff that you want and be on your merry way!