Here's how I just did it:
Install CMA, let it sync with your Vita using the Content Manager on the device, you now have PS Vita/PSAVEDATA in your "My Documents" folder. In it is a folder with a seemingly random name.
Get the exploited save file with the "TN-V" Custom Firmware (uncheck the download manager option, it's malware), either EU or US. The European version is just a folder named "ULES01515SAVE00" with some files in it. Put that folder in the aforementioned PS Vita/PSAVEDATA/*RANDOM NAME* folder.
Download
the official PSP firmware, rename it to "660.PBP" and put it in the "ULES01515SAVE00" folder (or US equivalent) which is now located in the seemingly randomly-named folder.
Go to your Vita > Content Management and copy the save file via Applications > PSP/Other after choosing PC > Vita. Exit the content manager, launch Gladiator Begins, load the save file in the game. When loaded, select the "Item Box" option. Your Vita now shows a white or green screen. Hold "R".
You're now in a menu. Go to Advanced > Install 6.60 files. Go back once it's done and choose Exit. Congrats, you can now do whatever you could do on a PSP with a custom firmware on it (e.g. homebrew).
To launch the PSP environment, just do Gladiator Begins > Save > Item Box again. You won't see the menu and instead boot directly into it.