To unlock the Fully Loaded trophy in Borderlands: Game of the Year Edition, you will need to collect 10 backpack upgrades and apply them manually. There are 10 backpack upgrades in the main story and 3 in the DLCs.
The locations will be highlighted with an exclamation mark on your map. You will visit each of the areas during the main story. The locations are listed below:
Main Story Locations:
The Lost Cave
The Salt Flats
Lumber Yard (at Jakobs Cove)
Lockdown Palace (in the Sunken Sea, accessible by travelling to T-Bone Junction and then through The Ridgeway)