DISCLAIMER: THIS FLASHES THE FLASH0 ON YOUR PSP, SO THERE IS A SMALL CHANCE OF BRICKING, DARK_ALEX, ME, NOR PSPMOD ARE RESPONSIBLE FOR ANY BRICKS
ONLY TRY THIS ON 1.50, 2.71 SE, 3.02 OE, 3.03 OE, or 3.10 OE FIRMWARE PSPs,
AND YES THIS WORKS ON TA-82s
3.30 OE-A Installation Tutorial!!! 
THIS UPGRADE WILL NOT WORK FOR PSPS WITH OFFICIAL SONY 3.10, 3.11, and 3.30 FIRMWARES INSTALLED
Description
*Basically its a custom firmware that has everything 3.30 has to offer and combines it with 1.5 homebrew capabilities and much more.
*It can be only installed as a full installation, due to some substantial changes in the bootstrap.
*Both, update maker and the flasher work in 1.50, 2.71 SE (whatever version), and 3.02/3.03/3.10 OE (whatever version)
*refer to the section below to see what has changed since Dark_Alexs last release
*If you want to see his last releases refer to here or here (Emulators)
Requirements
*your psp has to be a 1.5, 2.71 Se, 3.02 oe, 3.03 oe, 3.10 oe firmware installed on your psp
*Dont have a 1.5, 2.71 se, 3.02 oe, or 3.03 oe firmware psp?
*refer to the thread below
Ultimate Downgrader Thread (Madd Kat IS HERE)
*If you know what firmware and motherboard your psp has, refer to a corresponding thread
EASY 2.71 TA-82 DOWNGRADER
EASY 2.6/2.5 DOWNGRADER
EASY 2.71 DOWNGRADER
(which genesis emu for 3.03 oe-c)EASY 2.8-2.71 DOWNGRADER for TA-79, TA-82, and TA-86 motherboard PSPs
3.03 DOWNGRADER Tutorial (Anything wireless)
Whats changed from Dark_Alex's last custom firmware releases?
* Complete PSOne (PS1) game library support
* Homebrew supposrt under either 1.50 or 3.30 kernel
* Region spoofing
* Pached a protection that prevents the FW to load higher firmware modules
* Fixed a bug that could have caused instability in 3.10 OE after recovering from sleep mode
DAX says this doesn't support popsloader at the moment due to "Sony rearranging again the module list of pspbtcnf_pops", but rest assured that the great dev will be making a new version that will support all current pops in 3.10 OE, 3.30 OE and maybe 3.03 OE-C.
This Thread will Guide you on How to Install 3.30 OE-A
through two methods, The EASY Installer or Manually install
EASY Installer A.K.A NOOB proof (RECOMMENDED)
INSTRUCTIONS
Download 3.30 OE-A EASY FLASHER (Double click on pic)

sendspace download mirror
mediafire download mirror
Step 1) Copying files onto your psp
*Back up your psp files by coping them to your computer somewhere
*Format your memorystick
*Download "3.30 OE-A EASY FLASHER.rar" to your computer
*open it up and copy "330oeflasher" and "330oeflasher%" folders to the GAME(1.5 users) folder or GAME150(SE or OE firmware users) folder.
*NOTE - SE and OE firmware users must disable all their prxs in recovery mode, just a precaution, if you dont know what these are or dont have any dont worry about it you probably dont have any
Step 2) Running the EASY Flasher
*place your psp on its charger, and make sure your psp battery is 75% full or more (if its not the flasher wont run)
*go on your psp and run the "3.30 OE-A Firmware install" app.
*Follow the instructions and if all goes well you should have 3.30 OE-A
*Format you memory stick and recopy your backup psp files to your psp
NOTE - Hombrew go in the GAME150 folder
MANUAL INSTALL
How to install:
INTRUCTIONS it's pretty Easy.
Download
3.30 OE-A
1.50 Update Eboot
3.30 Update Eboot
*It can be only installed as a full installation, due to some substantial changes in the bootstrap.
*Both, update maker and the flasher work in 1.50, 2.71 SE (whatever version), and 3.02/3.03/3.10 OE (whatever version)
The instructions are as always:
*Copy oeupdmaker and oeupdmaker% to /PSP/GAME if you are in 1.50, or to /PSP/GAME150 if you are in
2.71 SE, 3.02 OE, 3.03 OE, or 3.10 OE.
*Get the 1.50 and 3.30 Sony updates, and put them in the oeupdatemaker folder with the names 150.PBP for the 1.50 eboot and 330.PBP for the 3.30 update.
*Execute the update maker. It will generate the dxar file.
Checksums of the generated file:
CRC32: A0723B56
MD5: DEBFC0488D088C384021231814514DA9
SHA1: 7AB9A6928BD08E26F9BEB18C3A2314AD0C745964
*Copy 330oeflasher and 330oeflasher% to /PSP/GAME if you are in 1.50, or to /PSP/GAME150 if you are in any SE/OE custom firmware psp. Move the DATA.DXAR you created to 330oeflasher directory.
*Execute the flasher and follow the instructions.
Extras
3.03 OE-C Plugins(these should work with 3.30 OE)
*refer to this thread
*this includes the plugins to listen to mp3s while you play a umd, the cheatdevice prxs, etc
How to use Recovery option
Download Recovery folder (Double click on pic)

Download mirror
Download mirror
Instructions
*Place folder in (PSP/GAME/RECOVERY) for Going back to 1.50 from any SE or OE firmware PSP
ok now
*turn PSP off (hold power switch for at least 10 sec)
*Turn PSP back on while holding "R" (you will get a Purple or Baby Blue Screen for 3.03oe-c screen this is the recovery main menu)
*Toggle the USB connectivity.(enable it) now transfer the recovery Folder to (if you haven't already) PSP/GAME/ after copying that Disable the USB
*Select the 3rd option " Run Program at PSP/GAME/RECOVERY/EBOOT.PBP" 6. Read the agreement, and follow the instructions
Best of luck to you. and you will have 1.50 soon
Other Useful Links
3.03 DOWNGRADER Tutorial (Anything wireless)
EASY 3.03 OE-C Custom Firmware Tutorial
EASY 3.03 OE-B CUSTOM FIRMWARE INSTALLER
EASY 3.02 OE-B CUSTOM FIRMWARE INSTALLER
Ultimate Downgrader Thread (Madd Kat IS HERE)
EASY 2.71 SE-C Installer
EASY 2.71 TA-82 DOWNGRADER
EASY 2.6/2.5 DOWNGRADER
EASY 2.71 DOWNGRADER
psp-updates
psp-hacks
Dark_AleX's official site