Noticed there wasn't one yet... so I decided to give psp a break and do it this time. I'm using psp's template because it's really good, hope you don't mind dude! Anyways, on with the show.
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, 3.10 OE, or 3.30 OE FIRMWARE PSP's!
AND YES, THIS WORKS ON TA-082's.
3.40 OE-A Installation Tutorial!!! 
THIS UPGRADE WILL NOT WORK FOR PSP's WITH OFFICIAL SONY 3.10, 3.11, 3.30, AND 3.40 FIRMWARES INSTALLED!! SO PLEASE, FOR THE SAKE OF OUR COLLECTIVE SANITY, STOP ASKING!!
Description
*Basically it's a custom firmware that has everything 3.40 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 3.02/3.03/3.10/3.30 OE (whatever version.)
*Refer to the section below to see what has changed since Dark_AleX's last release.
*If you want to see his last releases refer to
here or
here (Emulators).
Requirements
*Your PSP must have 1.5, 2.71 SE, 3.02 OE, 3.03 OE, 3.10 OE, or 3.30 OE firmware installed!
*Dont have a 1.5, 2.71 SE, 3.02 OE, 3.03 OE, 3.10 OE, or 3.30 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) What's changed from Dark_AleX's last custom firmware releases?
*Updated from 3.30 firmware to 3.40.
*Security patch: Fixed a bug that has been in all 3.XX OE, that caused random data to be written to a location in lcdc.prx or (in worst case) emc_sm.prx ram space.
*Autboot that is missing since 3.03 OE-C has been reimplemented.
Improvements in the flasher. It will now generate also the flash1 directories, and it will check that the dxar is the correct for this update, so no more bricks by accidentally using other DATA.DXAR.
(This still does not support Popsloader, so don't try it! However, it probably will pretty soon, so don't be afraid to upgrade either. ^^)
This Thread will Guide you on How to Install 3.40 OE-A
through two methods, The EASY Installer or Manual install
EASY Installer A.K.A NOOB proof (RECOMMENDED)
INSTRUCTIONS Download 3.40 OE-A EASY FLASHER 
http://darked.toddkleinert.com/files...asyFlasher.rar <-- Click here to get the file.
(NOTE: I took the Rapidshare/Megaupload mirrors down because they weren't working right. One of them was down completely and the other gave you 3.30 OE or somesuch. For now, just use my mirror.)
Mirrors uploaded by Blizzard182. Thanks a ton dude!
Step 1) Copying files onto your psp
*Back up your psp files by coping them to your computer somewhere
*Format your memorystick
*Download "3.40 OE-A EASY FLASHER.rar" to your computer
*Open it up and copy "340oeflasher" and "340oeflasher%" 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)
*Turn on your PSP and run the "3.40 OE-A Firmware install" app.
*Follow the instructions and if all goes well you should have 3.40 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 3.40 OE-A 1.50 Update Eboot 3.40 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 3.02/3.03/3.10/3.30 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, 3.10, or 3.30 OE.
*Get the
1.50 and
3.40 Sony updates, and put them in the oeupdatemaker folder with the names 150.PBP for the 1.50 eboot and 340.PBP for the 3.40 update.
*Execute the update maker. It will generate the dxar file.
Checksums of the generated file:
CRC32: CDA4638D
MD5: 9754F2CC0CBE2D8FE0DD009C90FDCD9F
SHA1: 6F76BB67B31EFF6FECB72D9D4AF443C793E1E521
*Copy 330oeflasher and 340oeflasher% 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 340oeflasher directory.
*Execute the flasher and follow the instructions.
Extras
3.03 OE-C Plugins(these should work with 3.40 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
Thanks to:
*psp for his OE firmware install tutorial template, I hope you don't mind me using it. If it's a problem, let me know, and I'll rewrite it. And another thing - changing all this info to reflect the new firmware version is a bitch! Props to you for doing it so many times man, seriously.
*Dark_AleX for all his dedication and all the time he spends hacking the PSP!
*Everyone here at PSPMod!