To earn this trophy you will need to build a weapon or mine on all build spots in a level, this includes the ones that you need to buy with barrels.
There is a way to unlock the areas you need to buy for free. Make sure you don't have enough barrels to buy the spot and press it, then press it again to buy it. Nothing will happen because you don't have enough barrels however if you open the start menu and press Restart, any of the spots you tried to buy will now be available as if you purchased them. Either do this or buy all of the spots in a level, build on them and the trophy will unlock.