I'd stay at 3.52 M33. It's not necessary to upgrade, but if you want to.
1. Find 3.71 M33 (go to Dark Alex's website). Do NOT download the M33-(number) updates yet!
2. Go to dl.qj.net (or somewhere) and find "1.50 Firmware". You should get a folder with an "eboot.pbp" inside it. Rename it "150.pbp (only name it 150 if file extensions aren't showing), and put it in the root folder (or inside the application itself, look to the readme). Put the "UPDATE" folder in the "PSP/GAME/" directory (without the quotes, of course).
3. Go into recovery mode (hold the "R" trigger on a cold boot), and go to "Configuration", "Game folder homebrew". Set it to 3.52 kernel and leave.
4. Go to the XMB and run the update. Make sure your PSP is plugged into the wall outlet, and then hole the L trigger and the triangle button (this bypasses the check for a battery at least at 75% percent charge). It will ask you about "IDstorage" and thiêgs about "keys." Hit the X button. A screen will come up that looks like a SONY updater, and it is, but it installs the custom firmware (pwned SONY). Agree to everything, it went quite slow for me, so give it a few minutes. When it says the update is done, PRESS X and let it reboot itself! It will brick if you turn it off!
The PSP will restart and you should be greeted with 3.71 M33. Go to the System Settings to make sure.
You should install the latest version of the custom firmware, and install the 1.50 patch. Find these (at Dark Alex's website), put them in the "PSP/GAME" folder. Put the 150.pbp file in the directory with the "PSP" folder in it (root directory). Run the "3.71 M33-4" update first. When that ends, run the "1.50 Kernal patcher." Once that ends, go into recovery mode, (configuration, Game folder homebrew) and set the kernal to 1.50. Then leave and play Super Mario War or something.
You should be done. Feel free to ask me questions.
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