1) Reflash their semi-bricked psp units
2) Downgrade from a higher custom firmware to a lower one.
3) Revert to an official firmware from a custom firmware
4) Upgrade directly to a new custom firmware from an older custom firmware without having to install the 3.52m33-4 firmware beforehand.
Here's a short and simple guide on how to get Hellcat's Flasher v1.60 on your psp unit.
1) Download Hellcat's Flasher 1.60 : Hellcat's Flasher 1.60
*Download the firmware of your choice only. For instance, if you want to install 5.00m33, then just download 500.pbp. Ignore the other firmwares*
2) Download 3.71 official firmware : 3.71 eboot
3) Download 3.80 official firmware : 3.80 eboot
4) Download 3.90 official firmware : 3.90 eboot
5) Download 4.01 official firmware : 4.01 eboot
6) Download 5.00 official firmware : 5.00 eboot
7) Once you've downloaded the flasher, extract the files and folders off the .rar file.
8) You should see a few folders. We want to concentrate on the one that is named RECOVERY as that is the folder that we will be using.
Note : To those whose psps are in a semi-bricked state, just boot into recovery mode, and enable USB mode there.
9) Copy the RECOVERY folder, and paste it in "ms0:/PSP/GAME"
10) Now, copy the firmware eboot that you downloaded, and paste it in the RECOVERY folder. After doing so, your directory should be something like this :
ms0:/PSP/GAME/RECOVERY/eboot.pbp and XXX.pbp (XXX represents the firmware name)
11) That's pretty much it. Now, just run it on your psp, and after that, everything is pretty much straight forward.