The 3.90 M33 firmware can only be installed once your PSP is already running the custom firmware 3.52 M33-4 or above.
And because you are already using a custom firmware you can directly install 3.52 M33 and then 3.52 M33-4. And once that is done you can then upgrade directly to 3.90 M33 and then to 3.90 M33-3.

The files you will need are:

For the 3.52 M33 upgrade.

  • 3.52 M33 upgrade installer
  • official Sony 1.5 firmware
  • official Sony 3.52 firmware
  • 3.52 M33-4 update

For the 3.90 M33 upgrade

  • 3.90 M33 upgrade installer
  • official Sony 3.90 firmware
  • 3.90 M33-3 update
  • 1.5 kernel addon V2 (not essential but adds ability to run FW1.5 homebrew and emulators on phat PSP)

You can download all of the custom installers from Dark Alex's own site found here or from QJ.net or from php-hacks. And you can get the official firmware downloads from here.

If you need more information or help on where to find all of these files please ask.