3-Updating/Reflashing/Downgrading CFW
Note:Before updating to any higher CFW , make a backup of all of your savedata in ms0:/PSP/SAVEDATA/ because updating might corrupt the savedata on your memory stick , so you have your backup , put it back to its place and the savedata will be no longer corrupted 
First : Updating CFW for hackable PSPS (PSP 1000 and PSP 2000 with non ta-088 v3)
Q:I wanna update my CFW
A:What CFW do you want to update to?
Q:What are the available custom firmwares ?
A:5.00 m33-6 and 5.50 gen-d3
From the names , 5.00 m33-6 is from a team but and 5.50 gen-d3 is from a same another team
5.00 m33-6 can't play 5.55+ games without patching , but patching is easy via my guide here
5.50 gen-d3 can play 5.55 , 6.00 and 6.10 games without patching .
However , there are still some problems in each of them
Pros of 5.00 m33-6 :
1-Speed up ms access feature
2-1.50 kernel add-on to play old homebrew
Pros of 5.50 gen-d3:
1-Playing new games without patching , also explained above
Cons of 5.00 m33-6 :
1-Unable to play newer games without patching , explained above
Cons of 5.50 gen-d3
1-No speed up ms feature ( Check my guide here and check adding the speed up feature , this adds a slightly slower but a good speed up )
2-No 1.50 kernel add-on , which means no old homebrew
3-Corrupting some savedata. . This problem is fixed by an app . see my guide
Notes for updating :
*If you wanna update to 5.00 M33-6 , just follow 'M33-6 Step'
*If you wanna update to 5.50 GEN-D3 , then your CFW must be 4.01 M33 or higher . If it's lower than that , then update to M33-6 first via 'M33-6 Step' then upgrade to 5.50 GEN-D3 via 'GEN-D3 Step'
'M33-6 Step'( To upgrade to 5.00 M33-6 from any CFW/To upgrade to 5.00 M33-6 from 1.50 OFW/ To downgrade from 5.50 GEN-A/B2/C/D/D2/D3 CFW to 5.00 M33-6/To reflash firmware for fixing problems )
NOTE: THIS IS ONLY FOR PHAT PSPS AND PSP 2000 WITH OLD HACKABLE NON TA-088 V3 MOBOS . DON'T ATTEMP TO TRY THIS ON A PSP 3000 OR A SLIM PSP WITH TA-088 V3 MOBO
1-Reboot to Recovery menu and go to configuration and make sure game folder homebrew is set to
3.XX if upgrading from any 3.XX CFW
4.XX if upgrading from any 4.XX CFW
5.XX if reflashing or upgrading another 5.XX CFW
5.XX if downgrading from 5.50 GEN-A/B2/C/D/D2/D3
3-Extract it
4-If you're on CFW : Copy the RECOVERY folder resulted from the extraction to :
ms0:/PSP/GAME/ (ms0 is your psp memory stick)
If you're on 1.50 OFW :Copy the two folders in FW1.50 to ms0:/PSP/GAME/
6-Extract it
7-It'll give you an EBOOT.PBP file
8-Rename that EBOOT.PBP to exactly '500.PBP' without the quotes
(NOTE : if the EBOOT.PBP file in your PC its name just shows as EBOOT , then rename it to '500' only)
9-Copy the renamed EBOOT to the root of your memory stick or RECOVERY folder in your PSP memory stick . Either way it works
10-Exit USB mode
11-Run Hellcat recovery flasher 1.6 from Game in XMB
13-Make sure that target FW is set to 5.XX
14-Select the option ( install CFW of version selected above )
15-It'll ask you if you wanna reset settings , i recommend you do that
16-It'll do the job on its own , wait for it to be done
17-When it's done , it'll prompt you to press any button to turn off your PSP
18-You'll notice that the power light is blinking , DON'T BE AFRAID and
DON'T DO ANYTHING , just wait and it'll reboot automatically or shut down.
19- You have just installed 5.00 M33-6 CFW !
20-When you're in XMB (PSP main menu) press select and change UMD ISO mode to M33 Driver or Sony NP9660 .
21-I recommend you format the memory stick from the PSP to create
folder structure
22-Enjoy!
Again a pic of hellcat recovery flasher :
'GEN-D3 Step'( Upgrading to 5.50 Gen-D3/Reflashing 5.50 Gen-D3 )
NOTE: THIS IS ONLY FOR PHAT PSPS AND PSP 2000 WITH OLD HACKABLE NON TA-088 V3 MOBOS . DON'T ATTEMP TO TRY THIS ON A PSP 3000 OR A SLIM PSP WITH TA-088 V3 MOBO
Instructions
1-Reboot to recovery , go to configuration and make sure game folder homebrew is set to 4.XX/5.XX ( I didn't say 3.XX because this program requires 4.01 M33 CFW at least to run )
3-Extract it
4-Copy the 550.PBP file to the root of your memory stick and UPDATE folder to ms0:/PSP/GAME ( ms0 is your memory stick )
5-Go run the program from Game in your XMB
6-Click Enter
7-Choose the first option
8-Wait for it to be done
9-When it's done it'll tell you to click X to reboot or 0 to shut down
10-While in XMB , press select and change UMD ISO mode to m33 driver or sony np9660
11-Format the memory stick from the PSP to create folder structure
12-I recommend you do what's in this guide to fix 5.50 GEN-D3 problems
Second : Updating CFW for unhackable PSPS ( PSP 2000 with ta-088 v3 and PSP 3000 )
See this guide and follow the section for updating CFW for unhackable PSPS