Okay this tut will tell u how to install 1.50 firmware on a slim!
Its very easy!

Step 1: Download TimeMachine v0.1 from google.

Step 2: Place the TimeMachine folder in your game directory (PSP>GAME)

Step 3: You'll need the official 150 and 340 EBOOT'S so just google that and then download them.

Step 4: You'll also need the 3.60 official EBOOT, but since it doesn't exist because 2000's came with it, just google a file called 360.PSAR and download.

Step 5: Rename all the EBOOT's to there respective names: 150.PBP, 340.PBP and 360.PSAR.

Step 6: Go to TimeMachine on your PSP and run the app.

Step 7: Select the first option when the menu comes up: Install IPLLOADER on PSP MS boot sector. They will only take about 5 secs.

Step 8: Click on Install 1.50 with HW 3.40 modules. This may take roughly a minute.

Step 9: If you want, you can install 3.60 M33, but this isn't required.

So basically what we have now done is installed the full firmware, but not to our NAND, but instead to our MEMSTICK. *NOTE* If you are installing this to a MMS (Magic) I don't think it will work.

Step 10: Now get out a Pandora Battery (Yes, you need a TOOL Battery) and hold down the O (Circle Button). Now put the Pandora Battery in your'e psp while still holding O. You're PSP Slim will boot up after a longer than normal boot-up time.

Congratulations! You're PSP Slim is now successfully running a PHAT firmware!