Best way to upgrade?

I have a ta-082 running factory 3.03. I have a battery in which I shorted c06 and r21 . Also I have the proper version of GTA LCS. What I want to know is what is the best way to change it to the latest 3.90m33 custom firmware. I know I have many ways I can do this but I want the best way so I will not brick it or run into issues with the ID KEYS.
Also I have another psp already running 3.90m33 custom firmware that I can use during the process.