There is a trophy for Bandit Six called "Feel the Power" that requires you to purchase 3 different power ups. I don't understand the requirement for this as I have not come across any way in which you can purchase power ups to begin with. It would be massively helpful if you could purchase power ups, but I have not been able to find anything like this. What is the requirement in order to unlock this trophy?
This description is a bit weird. You need to purchase the power-up upgrades. You are correct in that you can't actually purchase any power-ups. Purchase an upgrade for 3 distinct power-ups in the upgrade menu and you will get the trophy. I have a guide for this and all other trophies in the Bandit Six: Combined Arms Trophy guide