3.80M33-5 is out, but I will not even bother. As long as you are on 3.80M33-?, you might as well go for the latest 3.90M33. Yes, you will need the standard charge up to 78% power at least and plug in to power during upgrade.
Just download the following and put it into /PSP/GAME. Then select it and run. Depending on your PSP set, you will be prompt to press X or O to reboot. Do that to avoid bricking.